subject:(Fukaya categories)

University of California – Berkeley

1. Sylvan, Zachary Aaron. On partially wrapped Fukaya categories.

Degree: Mathematics, 2015, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/2s9850j8

► We define a new class of symplectic spaces called ``pumpkin domains'', which roughly speaking comprise a Liouville domain and a Liouville hypersurface of its boundary.… (more)

Subjects/Keywords: Mathematics; Floer homology; Fukaya categories; Mirror symmetry; Symplectic geometry

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APA (6^th Edition):

Sylvan, Z. A. (2015). On partially wrapped Fukaya categories. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/2s9850j8

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):

Sylvan, Zachary Aaron. “On partially wrapped Fukaya categories.” 2015. Thesis, University of California – Berkeley. Accessed March 05, 2021. http://www.escholarship.org/uc/item/2s9850j8.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sylvan, Zachary Aaron. “On partially wrapped Fukaya categories.” 2015. Web. 05 Mar 2021.

Vancouver:

Sylvan ZA. On partially wrapped Fukaya categories. [Internet] [Thesis]. University of California – Berkeley; 2015. [cited 2021 Mar 05]. Available from: http://www.escholarship.org/uc/item/2s9850j8.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sylvan ZA. On partially wrapped Fukaya categories. [Thesis]. University of California – Berkeley; 2015. Available from: http://www.escholarship.org/uc/item/2s9850j8

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

2. Jin, Xin. Symplectic approaches in geometric representation theory.

Degree: Mathematics, 2015, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/07t5s31b

► We study various topics lying in the crossroads of symplectic topology and geometric representation theory, with an emphasis on understanding central objects in geometric representation… (more)

Subjects/Keywords: Mathematics; Fukaya categories; geometric representation theory; Lagrangian branes; perverse sheaves; symplectic geometry; symplectomorphism groups

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

APA (6^th Edition):

Jin, X. (2015). Symplectic approaches in geometric representation theory. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/07t5s31b

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):

Jin, Xin. “Symplectic approaches in geometric representation theory.” 2015. Thesis, University of California – Berkeley. Accessed March 05, 2021. http://www.escholarship.org/uc/item/07t5s31b.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Jin, Xin. “Symplectic approaches in geometric representation theory.” 2015. Web. 05 Mar 2021.

Vancouver:

Jin X. Symplectic approaches in geometric representation theory. [Internet] [Thesis]. University of California – Berkeley; 2015. [cited 2021 Mar 05]. Available from: http://www.escholarship.org/uc/item/07t5s31b.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jin X. Symplectic approaches in geometric representation theory. [Thesis]. University of California – Berkeley; 2015. Available from: http://www.escholarship.org/uc/item/07t5s31b

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Cambridge

3. Zibrowius, C. B. On a Heegaard Floer theory for tangles.

Degree: PhD, 2017, University of Cambridge

URL: https://doi.org/10.17863/CAM.8706 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707791

► The purpose of this thesis is to define a “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e.… (more)

▼ The purpose of this thesis is to define a “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e. a Heegaard Floer homology HFT^ for tangles in the 3-ball. The decategorification of HFL^ is the classical Alexander polynomial for links; likewise, the decategorification of HFT^ gives a local version ∇ˢ of the Alexander polynomial. In the first chapter of this thesis, we give a purely combinatorial definition of this polynomial invariant ∇ˢ via Kauffman states and Alexander codes and investigate some of its properties. As an application, we show that the multivariate Alexander polynomial is mutation invariant. In the second chapter, we define HFT^ in two slightly different, but equivalent ways: One is via Juhász’s sutured Floer homology, the other by imitating the construction of HFL^. We then state a glueing theorem in terms of Zarev’s bordered sutured Floer homology, which endows HFT^ with additional structure. As an application, we show that any two links related by mutation about a (2,−3)-pretzel tangle have the same δ-graded link Floer homology. This result relies on a computer calculation. In the third and last chapter, we specialise to 4-ended tangles. In this case, we give a reformulation of HFT^ with a glueing structure in terms of (what we call) peculiar modules. Together with a glueing theorem, we can easily recover oriented and unoriented skein relations for HFL^. Our peculiar modules also enjoy some symmetry relations, which support a conjecture about δ-graded mutation invariance of HFL^. However, stronger symmetries would be needed to actually prove this conjecture. Finally, we explore the relationship between peculiar modules and twisted complexes in the wrapped Fukaya category of the 4-punctured sphere. There are four appendices, some of which might be of independent interest: In the first appendix, we describe a general construction of dg categories which unifies all algebraic structures used in this thesis, in particular type A and type D modules from bordered theory. In the second appendix, we prove a generalised version of Kauffman’s clock theorem, which plays a major role for our decategorified invariants. The last two appendices are manuals for two Mathematica programs. The first is a tool for computing the generators of HFT^ and the decategorified tangle invariant ∇ˢ. The second allows us to compute bordered sutured Floer homology using nice diagrams.

Subjects/Keywords: 516.3; Heegaard Floer homology; tangles; mutation; Alexander polynomial; categorification; Kauffman states; Fukaya categories; curved complexes; peculiar modules

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

APA (6^th Edition):

Zibrowius, C. B. (2017). On a Heegaard Floer theory for tangles. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.8706 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707791

Chicago Manual of Style (16^th Edition):

Zibrowius, C B. “On a Heegaard Floer theory for tangles.” 2017. Doctoral Dissertation, University of Cambridge. Accessed March 05, 2021. https://doi.org/10.17863/CAM.8706 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707791.

MLA Handbook (7^th Edition):

Zibrowius, C B. “On a Heegaard Floer theory for tangles.” 2017. Web. 05 Mar 2021.

Vancouver:

Zibrowius CB. On a Heegaard Floer theory for tangles. [Internet] [Doctoral dissertation]. University of Cambridge; 2017. [cited 2021 Mar 05]. Available from: https://doi.org/10.17863/CAM.8706 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707791.

Council of Science Editors:

Zibrowius CB. On a Heegaard Floer theory for tangles. [Doctoral Dissertation]. University of Cambridge; 2017. Available from: https://doi.org/10.17863/CAM.8706 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707791

Université de Montréal

4. Campling, Emily. Fukaya categories of Lagrangian cobordisms and duality.

Degree: 2019, Université de Montréal

URL: http://hdl.handle.net/1866/21746

Subjects/Keywords: symplectic topology; Lagrangian submanifolds; Floer homology; Fukaya categories; derived Fukaya categories; Lagrangian cobordisms; Lagrangian surgery; weak Calabi- Yau structures; Topologie symplectique; Sous-variétés lagrangiennes; Homologie de Floer; Catégories de Fukaya; Catégories de Fukaya dérivées; Cobordismes lagrangiens; Chirurgie lagrangienne; Structures de Calabi-Yau faibles; Mathematics / Mathématiques (UMI : 0405)

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

APA (6^th Edition):

Campling, E. (2019). Fukaya categories of Lagrangian cobordisms and duality. (Thesis). Université de Montréal. Retrieved from http://hdl.handle.net/1866/21746

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):

Campling, Emily. “Fukaya categories of Lagrangian cobordisms and duality.” 2019. Thesis, Université de Montréal. Accessed March 05, 2021. http://hdl.handle.net/1866/21746.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Campling, Emily. “Fukaya categories of Lagrangian cobordisms and duality.” 2019. Web. 05 Mar 2021.

Vancouver:

Campling E. Fukaya categories of Lagrangian cobordisms and duality. [Internet] [Thesis]. Université de Montréal; 2019. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1866/21746.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Campling E. Fukaya categories of Lagrangian cobordisms and duality. [Thesis]. Université de Montréal; 2019. Available from: http://hdl.handle.net/1866/21746

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

5. Zibrowius, Claudius. On a Heegaard Floer theory for tangles.

Degree: PhD, 2017, University of Cambridge

URL: https://www.repository.cam.ac.uk/handle/1810/263367https://www.repository.cam.ac.uk/bitstream/1810/263367/5/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/6/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/8/HDs.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/7/thesis.pdf.jpg ; https://www.repository.cam.ac.uk/bitstream/1810/263367/9/HDs.pdf.jpg

► The purpose of this thesis is to define a “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e.… (more)

▼ The purpose of this thesis is to define a “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e. a Heegaard Floer homology HFT^ for tangles in the 3-ball. The decategorification of HFL^ is the classical Alexander polynomial for links; likewise, the decategorification of HFT^ gives a local version ∇ˢ of the Alexander polynomial. In the first chapter of this thesis, we give a purely combinatorial definition of this polynomial invariant ∇ˢ via Kauffman states and Alexander codes and investigate some of its properties. As an application, we show that the multivariate Alexander polynomial is mutation invariant. In the second chapter, we define HFT^ in two slightly different, but equivalent ways: One is via Juhász’s sutured Floer homology, the other by imitating the construction of HFL^. We then state a glueing theorem in terms of Zarev’s bordered sutured Floer homology, which endows HFT^ with additional structure. As an application, we show that any two links related by mutation about a (2,−3)-pretzel tangle have the same δ-graded link Floer homology. This result relies on a computer calculation. In the third and last chapter, we specialise to 4-ended tangles. In this case, we give a reformulation of HFT^ with a glueing structure in terms of (what we call) peculiar modules. Together with a glueing theorem, we can easily recover oriented and unoriented skein relations for HFL^. Our peculiar modules also enjoy some symmetry relations, which support a conjecture about δ-graded mutation invariance of HFL^. However, stronger symmetries would be needed to actually prove this conjecture. Finally, we explore the relationship between peculiar modules and twisted complexes in the wrapped Fukaya category of the 4-punctured sphere. There are four appendices, some of which might be of independent interest: In the first appendix, we describe a general construction of dg categories which unifies all algebraic structures used in this thesis, in particular type A and type D modules from bordered theory. In the second appendix, we prove a generalised version of Kauffman’s clock theorem, which plays a major role for our decategorified invariants. The last two appendices are manuals for two Mathematica programs. The first is a tool for computing the generators of HFT^ and the decategorified tangle invariant ∇ˢ. The second allows us to compute bordered sutured Floer homology using nice diagrams.

Subjects/Keywords: Heegaard Floer homology; tangles; mutation; Alexander polynomial; categorification; Kauffman states; Fukaya categories; curved complexes; peculiar modules

…ended tangles Skein relations Symmetry relations for CFT∂ CFT∂ and the wrapped Fukaya category… …categories 97 Appendix B. Proof of the generalised clock theorem 105 Appendix C. Manual for… …us discuss bordered invariants in a little more detail. Bordered theory and Fukaya… …categories. In general, the invariants and the glueing theorems in bordered and also bordered… …algebra 4 INTRODUCTION A(F ) in terms of some partially wrapped Fukaya category…

1 more image…

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

APA (6^th Edition):

Zibrowius, C. (2017). On a Heegaard Floer theory for tangles. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/263367https://www.repository.cam.ac.uk/bitstream/1810/263367/5/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/6/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/8/HDs.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/7/thesis.pdf.jpg ; https://www.repository.cam.ac.uk/bitstream/1810/263367/9/HDs.pdf.jpg

Chicago Manual of Style (16^th Edition):

Zibrowius, Claudius. “On a Heegaard Floer theory for tangles.” 2017. Doctoral Dissertation, University of Cambridge. Accessed March 05, 2021. https://www.repository.cam.ac.uk/handle/1810/263367https://www.repository.cam.ac.uk/bitstream/1810/263367/5/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/6/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/8/HDs.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/7/thesis.pdf.jpg ; https://www.repository.cam.ac.uk/bitstream/1810/263367/9/HDs.pdf.jpg.

MLA Handbook (7^th Edition):

Zibrowius, Claudius. “On a Heegaard Floer theory for tangles.” 2017. Web. 05 Mar 2021.

Vancouver:

Zibrowius C. On a Heegaard Floer theory for tangles. [Internet] [Doctoral dissertation]. University of Cambridge; 2017. [cited 2021 Mar 05]. Available from: https://www.repository.cam.ac.uk/handle/1810/263367https://www.repository.cam.ac.uk/bitstream/1810/263367/5/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/6/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/8/HDs.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/7/thesis.pdf.jpg ; https://www.repository.cam.ac.uk/bitstream/1810/263367/9/HDs.pdf.jpg.

Council of Science Editors:

Zibrowius C. On a Heegaard Floer theory for tangles. [Doctoral Dissertation]. University of Cambridge; 2017. Available from: https://www.repository.cam.ac.uk/handle/1810/263367https://www.repository.cam.ac.uk/bitstream/1810/263367/5/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/6/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/8/HDs.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/263367/7/thesis.pdf.jpg ; https://www.repository.cam.ac.uk/bitstream/1810/263367/9/HDs.pdf.jpg

6. Perrier, Alexandre. Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes.

Degree: 2019, Université de Montréal

URL: http://hdl.handle.net/1866/21747

Subjects/Keywords: Immersions lagrangiennes; Polygones holomorphes; Cobordismes Lagrangiens; Groupes de cobordisme; Homologie de Floer; Catégories de Fukaya; Sous-variétés lagrangiennes; Lagrangian submanifolds; Lagrangian immersions; Holomorphic polygons; Lagrangian cobordisms; Cobordism groups; Floer homology; Fukaya categories; Mathematics / Mathématiques (UMI : 0405)

…101 2.3. Fukaya categories of surfaces… …119 2.3.3. Properties of the Fukaya category… …Donaldson-Fukaya est un invariant peu pratique pour plusieurs raisons. (A) Il n’est pas… …qui est perdue par ce passage au quotient2. Pour régler le problème (B), Fukaya… …définition plus haut. Malheureusement cette application n’est pas associative. Fukaya remarque…

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

APA (6^th Edition):

Perrier, A. (2019). Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes. (Thesis). Université de Montréal. Retrieved from http://hdl.handle.net/1866/21747

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):

Perrier, Alexandre. “Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes.” 2019. Thesis, Université de Montréal. Accessed March 05, 2021. http://hdl.handle.net/1866/21747.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Perrier, Alexandre. “Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes.” 2019. Web. 05 Mar 2021.

Vancouver:

Perrier A. Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes. [Internet] [Thesis]. Université de Montréal; 2019. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1866/21747.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Perrier A. Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes. [Thesis]. Université de Montréal; 2019. Available from: http://hdl.handle.net/1866/21747

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Université de Montréal

7. Charest, François. Source spaces and perturbations for cluster complexes.

Degree: 2012, Université de Montréal

URL: http://hdl.handle.net/1866/8998

Subjects/Keywords: Topologie symplectique; Catégories de Fukaya; Sous-variétés lagrangiennes; Homologie de Floer; Homologie de Morse; Homologie des clusters; Clusters; Courbes pseudoholomorphes; Transversalité; Voisinage collier; Symplectic topology; Fukaya categories; Lagrangian submanifolds; Floer homology; Morse homology; Cluster homology; Clusters; Pseudoholomorphic curves; Regularity; Collar neighborhood; Mathematics / Mathématiques (UMI : 0405)

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

APA (6^th Edition):

Charest, F. (2012). Source spaces and perturbations for cluster complexes. (Thesis). Université de Montréal. Retrieved from http://hdl.handle.net/1866/8998

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):

Charest, François. “Source spaces and perturbations for cluster complexes.” 2012. Thesis, Université de Montréal. Accessed March 05, 2021. http://hdl.handle.net/1866/8998.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Charest, François. “Source spaces and perturbations for cluster complexes.” 2012. Web. 05 Mar 2021.

Vancouver:

Charest F. Source spaces and perturbations for cluster complexes. [Internet] [Thesis]. Université de Montréal; 2012. [cited 2021 Mar 05]. Available from: http://hdl.handle.net/1866/8998.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Charest F. Source spaces and perturbations for cluster complexes. [Thesis]. Université de Montréal; 2012. Available from: http://hdl.handle.net/1866/8998

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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