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Symplectic cohomology and duality for the wrapped Fukaya Category

Author(s)
Ganatra, Sheel (Sheel Chandrakant)
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Denis Auroux.
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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
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Abstract
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.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (p. 313-315).
 
Date issued
2012
URI
http://hdl.handle.net/1721.1/73362
Department
Massachusetts Institute of Technology. Dept. of Mathematics.
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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  • Mathematics - Ph.D. / Sc.D.
  • Mathematics - Ph.D. / Sc.D.

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