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1.
Beheshti Vadeqan, Babak.
Geometry of *Dirac* * Operators*
.

Degree: Mathematics and Statistics, 2016, Queens University

URL: http://hdl.handle.net/1974/14633

► Let M be a compact, oriented, even dimensional Riemannian manifold and let S be a Clifford bundle over M with *Dirac* operator D. Then […
(more)

Subjects/Keywords: Atiyah-Singer Index Theorem ; Dirac Operators ; Elliptic Geometry

…this thesis to show that elliptic *operators* and specifically *Dirac* *operators*
contain certain… …*Dirac* *operators*.
We shall also see that the study of *Dirac* *operators* reveals some… …a more general type of elliptic differential *operators* which are said to be *Dirac* type… …*operators* called *Dirac*
*operators*. In this thesis we are planning to study this type of *operators*… …*Dirac* *operators* on manifolds. We will start by introducing Clifford algebras and their…

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APA (6^{th} Edition):

Beheshti Vadeqan, B. (2016). Geometry of Dirac Operators . (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/14633

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Beheshti Vadeqan, Babak. “Geometry of Dirac Operators .” 2016. Thesis, Queens University. Accessed January 19, 2021. http://hdl.handle.net/1974/14633.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Beheshti Vadeqan, Babak. “Geometry of Dirac Operators .” 2016. Web. 19 Jan 2021.

Vancouver:

Beheshti Vadeqan B. Geometry of Dirac Operators . [Internet] [Thesis]. Queens University; 2016. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/1974/14633.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Beheshti Vadeqan B. Geometry of Dirac Operators . [Thesis]. Queens University; 2016. Available from: http://hdl.handle.net/1974/14633

Not specified: Masters Thesis or Doctoral Dissertation

ETH Zürich

2.
Farinelli, S.
Spectra of *dirac* *operators* on a family of degenerating hyperbolic three manifolds.

Degree: 1998, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/143641

Subjects/Keywords: DIRAC-OPERATOREN (FUNKTIONALANALYSIS); RIEMANNSCHE MANNIGFALTIGKEITEN (TOPOLOGIE); DIRAC OPERATORS (FUNCTIONAL ANALYSIS); RIEMANNIAN MANIFOLDS (TOPOLOGY); info:eu-repo/classification/ddc/510; info:eu-repo/classification/ddc/510; info:eu-repo/classification/ddc/510; Mathematics; Mathematics; Mathematics

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APA (6^{th} Edition):

Farinelli, S. (1998). Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/143641

Chicago Manual of Style (16^{th} Edition):

Farinelli, S. “Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.” 1998. Doctoral Dissertation, ETH Zürich. Accessed January 19, 2021. http://hdl.handle.net/20.500.11850/143641.

MLA Handbook (7^{th} Edition):

Farinelli, S. “Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.” 1998. Web. 19 Jan 2021.

Vancouver:

Farinelli S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. [Internet] [Doctoral dissertation]. ETH Zürich; 1998. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/20.500.11850/143641.

Council of Science Editors:

Farinelli S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. [Doctoral Dissertation]. ETH Zürich; 1998. Available from: http://hdl.handle.net/20.500.11850/143641

3. Klaasse, R.L. Seiberg-Witten theory for symplectic manifolds.

Degree: 2013, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/282753

► In this thesis we give an introduction to Seiberg-Witten gauge theory used to study compact oriented four-dimensional manifolds X. Seiberg-Witten theory uses a Spin c…
(more)

Subjects/Keywords: Seiberg-Witten theory; four-manifolds; symplectic manifolds; Spin c structures; Dirac operators

…forms,
so that we are done.
2.4
Elliptic *operators*
In this section we discuss the notion of… …analogous notion for *operators* between sections of vector bundles.
Definition 2.4.2. An operator D… …of Fredholm *operators* is that their index is invariant under perturbations.
In other words… …if one were to take a family of Fredholm *operators* parameterized by some
connected… …Fredholmness of *operators* and calculating their index. A key concept is that of
ellipticity. Let π…

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APA (6^{th} Edition):

Klaasse, R. L. (2013). Seiberg-Witten theory for symplectic manifolds. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/282753

Chicago Manual of Style (16^{th} Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Masters Thesis, Universiteit Utrecht. Accessed January 19, 2021. http://dspace.library.uu.nl:8080/handle/1874/282753.

MLA Handbook (7^{th} Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Web. 19 Jan 2021.

Vancouver:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Internet] [Masters thesis]. Universiteit Utrecht; 2013. [cited 2021 Jan 19]. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753.

Council of Science Editors:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Masters Thesis]. Universiteit Utrecht; 2013. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753

University of Michigan

4. Korpas, Levente. Quantization of symplectic cobordisms.

Degree: PhD, Pure Sciences, 1999, University of Michigan

URL: http://hdl.handle.net/2027.42/131922

► In this work we construct a unitary operator acting between Spin^{ c} quantizations of compact integral symplectic manifolds which are symplectically cobordant. The construction is…
(more)

Subjects/Keywords: Cobordisms; Dirac Operators; Quantization; Symplectic Manifolds

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APA (6^{th} Edition):

Korpas, L. (1999). Quantization of symplectic cobordisms. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/131922

Chicago Manual of Style (16^{th} Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Doctoral Dissertation, University of Michigan. Accessed January 19, 2021. http://hdl.handle.net/2027.42/131922.

MLA Handbook (7^{th} Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Web. 19 Jan 2021.

Vancouver:

Korpas L. Quantization of symplectic cobordisms. [Internet] [Doctoral dissertation]. University of Michigan; 1999. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/2027.42/131922.

Council of Science Editors:

Korpas L. Quantization of symplectic cobordisms. [Doctoral Dissertation]. University of Michigan; 1999. Available from: http://hdl.handle.net/2027.42/131922

5. Lal, Nishu. Spectral Zeta Functions of Laplacians on Self-Similar Fractals.

Degree: Mathematics, 2012, University of California – Riverside

URL: http://www.escholarship.org/uc/item/888903d2

► This thesis investigates the spectral zeta function of fractal differential *operators* such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar…
(more)

Subjects/Keywords: Mathematics; Analysis on fractals; decimation method; Dirac delta hyperfunction; fractal Sturm-Liouville operators; multivariable complex dynamics; spectral zeta functions

…the spectral zeta function of fractal differential *operators* such
as the Laplacian on the… …the spectral zeta function of such an operator,
expressed in terms of the *Dirac* delta… …variables associated
with fractal Sturm–Liouville *operators*. Moreover, as a corollary, in the very… …Adjoint *Operators* and Quadratic Forms . . . . . .
2.5 Introduction To Hyperfunctions… …3.3.1 Main Lemma Regarding the *Dirac* Delta Hyperfunction . . . . .
3.4 A Representation of the…

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APA (6^{th} Edition):

Lal, N. (2012). Spectral Zeta Functions of Laplacians on Self-Similar Fractals. (Thesis). University of California – Riverside. Retrieved from http://www.escholarship.org/uc/item/888903d2

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Thesis, University of California – Riverside. Accessed January 19, 2021. http://www.escholarship.org/uc/item/888903d2.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Web. 19 Jan 2021.

Vancouver:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Internet] [Thesis]. University of California – Riverside; 2012. [cited 2021 Jan 19]. Available from: http://www.escholarship.org/uc/item/888903d2.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Thesis]. University of California – Riverside; 2012. Available from: http://www.escholarship.org/uc/item/888903d2

Not specified: Masters Thesis or Doctoral Dissertation

Loughborough University

6.
Li, Liangpan.
Local spectral asymptotics and heat kernel bounds for *Dirac* and Laplace * operators*.

Degree: PhD, 2016, Loughborough University

URL: http://hdl.handle.net/2134/23004

► In this dissertation we study non-negative self-adjoint Laplace type *operators* acting on smooth sections of a vector bundle. First, we assume base manifolds are compact,…
(more)

Subjects/Keywords: 515; Local spectral asymptotics; Heat kernel; Dirac operators; Laplace operators; Pseudo-differential operators; Fourier integral operators; Wodzicki residue; Finite propagation speed; Spectral determinant

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Li, L. (2016). Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. (Doctoral Dissertation). Loughborough University. Retrieved from http://hdl.handle.net/2134/23004

Chicago Manual of Style (16^{th} Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Doctoral Dissertation, Loughborough University. Accessed January 19, 2021. http://hdl.handle.net/2134/23004.

MLA Handbook (7^{th} Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Web. 19 Jan 2021.

Vancouver:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Internet] [Doctoral dissertation]. Loughborough University; 2016. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/2134/23004.

Council of Science Editors:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Doctoral Dissertation]. Loughborough University; 2016. Available from: http://hdl.handle.net/2134/23004

Michigan State University

7.
Maridakis, Manousos.
The concentration principle for *Dirac* * operators*.

Degree: 2014, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:2604

►

Thesis Ph. D. Michigan State University. Mathematics 2014.

The symbol map σ of an elliptic operator carries essential topological and geometrical information about the underlying… (more)

Subjects/Keywords: Dirac equation; Manifolds (Mathematics); Differential operators; Theoretical mathematics

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APA (6^{th} Edition):

Maridakis, M. (2014). The concentration principle for Dirac operators. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:2604

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Maridakis, Manousos. “The concentration principle for Dirac operators.” 2014. Thesis, Michigan State University. Accessed January 19, 2021. http://etd.lib.msu.edu/islandora/object/etd:2604.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Maridakis, Manousos. “The concentration principle for Dirac operators.” 2014. Web. 19 Jan 2021.

Vancouver:

Maridakis M. The concentration principle for Dirac operators. [Internet] [Thesis]. Michigan State University; 2014. [cited 2021 Jan 19]. Available from: http://etd.lib.msu.edu/islandora/object/etd:2604.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Maridakis M. The concentration principle for Dirac operators. [Thesis]. Michigan State University; 2014. Available from: http://etd.lib.msu.edu/islandora/object/etd:2604

Not specified: Masters Thesis or Doctoral Dissertation

Australian National University

8.
Morris, Andrew Jordan.
Local Hardy spaces and quadratic estimates for *Dirac* type *operators* on Riemannian manifolds
.

Degree: 2010, Australian National University

URL: http://hdl.handle.net/1885/8864

► The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to…
(more)

Subjects/Keywords: holomorphic functional calculi; quadratic estimates; sectorial operators; local Hardy spaces; Riemannian manifolds; differential forms; Hodge – Dirac operators; local Riesz transforms; off-diagonal estimates; Davies – Gaffney estimates; Kato square-root problems; submanifolds; divergence form operators; first-order differential operators

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APA (6^{th} Edition):

Morris, A. J. (2010). Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/8864

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Morris, Andrew Jordan. “Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .” 2010. Thesis, Australian National University. Accessed January 19, 2021. http://hdl.handle.net/1885/8864.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Morris, Andrew Jordan. “Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .” 2010. Web. 19 Jan 2021.

Vancouver:

Morris AJ. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . [Internet] [Thesis]. Australian National University; 2010. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/1885/8864.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Morris AJ. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . [Thesis]. Australian National University; 2010. Available from: http://hdl.handle.net/1885/8864

Not specified: Masters Thesis or Doctoral Dissertation

Indian Institute of Science

9. Rahaman, Md Aminoor. Search On A Hypercubic Lattice Using Quantum Random Walk.

Degree: MSc Engg, Faculty of Engineering, 2010, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/972

► Random walks describe diffusion processes, where movement at every time step is restricted only to neighbouring locations. Classical random walks are constructed using the non-relativistic…
(more)

Subjects/Keywords: Lattice Theory - Data Processing; Quantum Random Walk; Grover's Algorithm; Dirac Operators; Quantum Computation; Dimensional Hypercubic Lattices; Random Walk Algorithm; Spatial Search; Quantum Physics

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APA (6^{th} Edition):

Rahaman, M. A. (2010). Search On A Hypercubic Lattice Using Quantum Random Walk. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/972

Chicago Manual of Style (16^{th} Edition):

Rahaman, Md Aminoor. “Search On A Hypercubic Lattice Using Quantum Random Walk.” 2010. Masters Thesis, Indian Institute of Science. Accessed January 19, 2021. http://etd.iisc.ac.in/handle/2005/972.

MLA Handbook (7^{th} Edition):

Rahaman, Md Aminoor. “Search On A Hypercubic Lattice Using Quantum Random Walk.” 2010. Web. 19 Jan 2021.

Vancouver:

Rahaman MA. Search On A Hypercubic Lattice Using Quantum Random Walk. [Internet] [Masters thesis]. Indian Institute of Science; 2010. [cited 2021 Jan 19]. Available from: http://etd.iisc.ac.in/handle/2005/972.

Council of Science Editors:

Rahaman MA. Search On A Hypercubic Lattice Using Quantum Random Walk. [Masters Thesis]. Indian Institute of Science; 2010. Available from: http://etd.iisc.ac.in/handle/2005/972

10. Reynolds, Paul. On conformal submersions and manifolds with exceptional structure groups.

Degree: PhD, 2012, University of Edinburgh

URL: http://hdl.handle.net/1842/6218

► This thesis comes in three main parts. In the first of these (comprising chapters 2 - 6), the basic theory of Riemannian and conformal submersions…
(more)

Subjects/Keywords: 519; Riemannian submersions; conformal submersions; Clifford algebra; spinor bundles; Dirac operators; quaternionic-Kahler quotients

…56
6 *Dirac* *Operators* and Conformal
6.1 *Dirac* operator formulae . . . .
6.2 One-dimensional… …distribution V
The mean curvature of the horizontal distribution H
Various *Dirac* *operators*
The real… …next step is to calculate
expressions for the *Dirac* *operators*. This does not require us to… …on M constructed from these.
The *Dirac* *operators* of the total space, base and fibres are… …Calculation of the *Dirac* *operators* and application to the characterisation of
*Dirac* morphisms.
8…

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APA (6^{th} Edition):

Reynolds, P. (2012). On conformal submersions and manifolds with exceptional structure groups. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/6218

Chicago Manual of Style (16^{th} Edition):

Reynolds, Paul. “On conformal submersions and manifolds with exceptional structure groups.” 2012. Doctoral Dissertation, University of Edinburgh. Accessed January 19, 2021. http://hdl.handle.net/1842/6218.

MLA Handbook (7^{th} Edition):

Reynolds, Paul. “On conformal submersions and manifolds with exceptional structure groups.” 2012. Web. 19 Jan 2021.

Vancouver:

Reynolds P. On conformal submersions and manifolds with exceptional structure groups. [Internet] [Doctoral dissertation]. University of Edinburgh; 2012. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/1842/6218.

Council of Science Editors:

Reynolds P. On conformal submersions and manifolds with exceptional structure groups. [Doctoral Dissertation]. University of Edinburgh; 2012. Available from: http://hdl.handle.net/1842/6218

Université de Bordeaux I

11. Sambou, Diomba. Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians.

Degree: Docteur es, Mathématiques appliquées et calcul scientifique, 2013, Université de Bordeaux I

URL: http://www.theses.fr/2013BOR14906

►

Dans cette thèse on s'interesse à l'étude de phénomènes d'accumultation spectrale de certains opérateurs issus de la physique quantique à savoir les opérateurs de Schrödinger,… (more)

Subjects/Keywords: Opérateurs de Schrödinger; Opérateurs de Pauli; Opérateurs de Dirac magnétiques,; Résonances; Inégalités Lieb-Thirring généralisées.; Magnetic Schrödinger; Dirac operators; Pauli operatoirs; Resonances; Generalized Lieb-Thirring inequalities

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Sambou, D. (2013). Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians. (Doctoral Dissertation). Université de Bordeaux I. Retrieved from http://www.theses.fr/2013BOR14906

Chicago Manual of Style (16^{th} Edition):

Sambou, Diomba. “Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians.” 2013. Doctoral Dissertation, Université de Bordeaux I. Accessed January 19, 2021. http://www.theses.fr/2013BOR14906.

MLA Handbook (7^{th} Edition):

Sambou, Diomba. “Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians.” 2013. Web. 19 Jan 2021.

Vancouver:

Sambou D. Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians. [Internet] [Doctoral dissertation]. Université de Bordeaux I; 2013. [cited 2021 Jan 19]. Available from: http://www.theses.fr/2013BOR14906.

Council of Science Editors:

Sambou D. Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians. [Doctoral Dissertation]. Université de Bordeaux I; 2013. Available from: http://www.theses.fr/2013BOR14906

University of Michigan

12.
Sandoval, Mary Ruth.
Wave-trace asymptotics for *operators* of *Dirac* type.

Degree: PhD, Pure Sciences, 1997, University of Michigan

URL: http://hdl.handle.net/2027.42/130578

► Spectral geometry seeks to understand the relationship between the spectra of differential *operators* and the underlying geometry of a manifold, especially to understand which geometric…
(more)

Subjects/Keywords: Asymptotics; Dirac; Operators; Spectral Geometry; Trace; Type; Wave

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APA (6^{th} Edition):

Sandoval, M. R. (1997). Wave-trace asymptotics for operators of Dirac type. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/130578

Chicago Manual of Style (16^{th} Edition):

Sandoval, Mary Ruth. “Wave-trace asymptotics for operators of Dirac type.” 1997. Doctoral Dissertation, University of Michigan. Accessed January 19, 2021. http://hdl.handle.net/2027.42/130578.

MLA Handbook (7^{th} Edition):

Sandoval, Mary Ruth. “Wave-trace asymptotics for operators of Dirac type.” 1997. Web. 19 Jan 2021.

Vancouver:

Sandoval MR. Wave-trace asymptotics for operators of Dirac type. [Internet] [Doctoral dissertation]. University of Michigan; 1997. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/2027.42/130578.

Council of Science Editors:

Sandoval MR. Wave-trace asymptotics for operators of Dirac type. [Doctoral Dissertation]. University of Michigan; 1997. Available from: http://hdl.handle.net/2027.42/130578

University of Waterloo

13.
Suan, Caleb.
Differential *Operators* on Manifolds with G2-Structure.

Degree: 2020, University of Waterloo

URL: http://hdl.handle.net/10012/16565

► In this thesis, we study differential *operators* on manifolds with torsion-free G2-structure. In particular, we use an identification of the spinor bundle S of such…
(more)

Subjects/Keywords: differential geometry; G2-structures; twisted Dirac operator; differential operators

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APA (6^{th} Edition):

Suan, C. (2020). Differential Operators on Manifolds with G2-Structure. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/16565

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Suan, Caleb. “Differential Operators on Manifolds with G2-Structure.” 2020. Thesis, University of Waterloo. Accessed January 19, 2021. http://hdl.handle.net/10012/16565.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Suan, Caleb. “Differential Operators on Manifolds with G2-Structure.” 2020. Web. 19 Jan 2021.

Vancouver:

Suan C. Differential Operators on Manifolds with G2-Structure. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/10012/16565.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Suan C. Differential Operators on Manifolds with G2-Structure. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/16565

Not specified: Masters Thesis or Doctoral Dissertation

14. Takata, Doman. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .

Degree: 2018, Kyoto University

URL: http://hdl.handle.net/2433/232217

Subjects/Keywords: infinite-dimensional manifolds; loop groups; Dirac operators; assembly maps; KK-theory; index theory

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APA (6^{th} Edition):

Takata, D. (2018). A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/232217

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Thesis, Kyoto University. Accessed January 19, 2021. http://hdl.handle.net/2433/232217.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Web. 19 Jan 2021.

Vancouver:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Internet] [Thesis]. Kyoto University; 2018. [cited 2021 Jan 19]. Available from: http://hdl.handle.net/2433/232217.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Thesis]. Kyoto University; 2018. Available from: http://hdl.handle.net/2433/232217

Not specified: Masters Thesis or Doctoral Dissertation