2026-09-21T02:05:04Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/733622022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Denis Auroux.
Ganatra, Sheel (Sheel Chandrakant)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2012-09-27T15:25:32Z
2012-09-27T15:25:32Z
2012
2012
http://hdl.handle.net/1721.1/73362
809643051
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.
315 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Symplectic cohomology and duality for the wrapped Fukaya Category
Thesis
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Publication
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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.</Abstract>
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