Symplectic cohomology and duality for the wrapped Fukaya Category
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2012
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| Online Access: | http://hdl.handle.net/1721.1/73362 |
| _version_ | 1811070091429675008 |
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| author | Ganatra, Sheel (Sheel Chandrakant) |
| author2 | Denis Auroux. |
| author_facet | Denis Auroux. Ganatra, Sheel (Sheel Chandrakant) |
| author_sort | Ganatra, Sheel (Sheel Chandrakant) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. |
| first_indexed | 2024-09-23T08:24:01Z |
| format | Thesis |
| id | mit-1721.1/73362 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:24:01Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/733622019-04-09T18:13:43Z Symplectic cohomology and duality for the wrapped Fukaya Category Ganatra, Sheel (Sheel Chandrakant) Denis Auroux. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. Cataloged from PDF version of thesis. Includes bibliographical references (p. 313-315). Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from the Hochschild homology of W to symplectic cohomology and from symplectic cohomology to the Hochschild cohomology of W are isomorphisms, in a manner compatible with ring and module structures. This is a consequence of a more general duality for the wrapped Fukaya category, which should be thought of as a non-compact version of a Calabi-Yau structure. The new ingredients are: (1) Fourier-Mukai theory for W via a wrapped version of holomorphic quilts, (2) new geometric operations, coming from discs with two negative punctures and arbitrary many positive punctures, (3) a generalization of the Cardy condition, and (4) the use of homotopy units and A-infinity shuffle products to relate non-degeneracy to a resolution of the diagonal. by Sheel Ganatra. Ph.D. 2012-09-27T15:25:32Z 2012-09-27T15:25:32Z 2012 2012 Thesis http://hdl.handle.net/1721.1/73362 809643051 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 315 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Ganatra, Sheel (Sheel Chandrakant) Symplectic cohomology and duality for the wrapped Fukaya Category |
| title | Symplectic cohomology and duality for the wrapped Fukaya Category |
| title_full | Symplectic cohomology and duality for the wrapped Fukaya Category |
| title_fullStr | Symplectic cohomology and duality for the wrapped Fukaya Category |
| title_full_unstemmed | Symplectic cohomology and duality for the wrapped Fukaya Category |
| title_short | Symplectic cohomology and duality for the wrapped Fukaya Category |
| title_sort | symplectic cohomology and duality for the wrapped fukaya category |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/73362 |
| work_keys_str_mv | AT ganatrasheelsheelchandrakant symplecticcohomologyanddualityforthewrappedfukayacategory |