Symplectic cohomology and duality for the wrapped Fukaya Category
Name
809643051-MIT.pdf
Description
Full printable version
Size
14.86 MB
Format
Adobe PDF
Checksum (MD5)
a24a894f6d03c609be83435c2292b949
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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