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Symplectic cohomology and duality for the wrapped Fukaya Category

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Author(s)
Ganatra, Sheel (Sheel Chandrakant)
Advisor(s)
Denis Auroux.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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