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University of Michigan

1. Korpas, Levente. Quantization of symplectic cobordisms.

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

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 based on a recent proof of the cobordism invariance of the index of Dirac operators, due to L. Nicolaescu. We prove that, away from a small set on the boundary manifolds, this quantized cobordism operator is an Hermite-Fourier integral operator in the sense of L. Boutet de Monvel and V. Guillemin. The proof consists of two parts. In the first we show that the Spin c Szego&huml; projector, II, which defines the quantization, is itself an Hermite-Fourier integral operator just as in the well studied case of Kahler quantization. In the second part we explicitly construct the fundamental solution, K, of a boundary value problem for a transversally elliptic Dirac operator on a principal circle bundle over the cobordism. This construction is carried out within the category of Hermite-Fourier distributions and relies on their symbolic properties. For example, the transport equations are evolutions equations on <blkbd>R2n,</blkbd> in contrast with the case of Lagrangian distributions where they are ordinary differential equations. The microlocal structure of the quantized cobordism operator is the same as that of the composition P&j0;g&j0;K, where gamma is the boundary restriction operator. From the composition theorems for Hermite-Fourier integral operators it follows that P&j0;g&j0;K is an Hermite-FIO. In the last part of this work we present examples where our construction applies. Advisors/Committee Members: Uribe, Alejandro (advisor).

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

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

APA (6th 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 (16th Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Doctoral Dissertation, University of Michigan. Accessed March 05, 2021. http://hdl.handle.net/2027.42/131922.

MLA Handbook (7th Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Web. 05 Mar 2021.

Vancouver:

Korpas L. Quantization of symplectic cobordisms. [Internet] [Doctoral dissertation]. University of Michigan; 1999. [cited 2021 Mar 05]. 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

2. Hensel, Felix. Stability Conditions and Lagrangian Cobordisms.

Degree: 2018, ETH Zürich

Subjects/Keywords: Symplectic geometry; Lagrangian cobordisms; info:eu-repo/classification/ddc/510; Mathematics

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

APA (6th Edition):

Hensel, F. (2018). Stability Conditions and Lagrangian Cobordisms. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/281401

Chicago Manual of Style (16th Edition):

Hensel, Felix. “Stability Conditions and Lagrangian Cobordisms.” 2018. Doctoral Dissertation, ETH Zürich. Accessed March 05, 2021. http://hdl.handle.net/20.500.11850/281401.

MLA Handbook (7th Edition):

Hensel, Felix. “Stability Conditions and Lagrangian Cobordisms.” 2018. Web. 05 Mar 2021.

Vancouver:

Hensel F. Stability Conditions and Lagrangian Cobordisms. [Internet] [Doctoral dissertation]. ETH Zürich; 2018. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/20.500.11850/281401.

Council of Science Editors:

Hensel F. Stability Conditions and Lagrangian Cobordisms. [Doctoral Dissertation]. ETH Zürich; 2018. Available from: http://hdl.handle.net/20.500.11850/281401

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