Abstract/Details

Symplectic Cohomology and Duality for the Wrapped Fukaya Category

Ganatra, Sheel.   Massachusetts Institute of Technology ProQuest Dissertations Publishing,  2012. 0828785.

Abstract (summary)

Consider the wrapped Fukaya category [special characters omitted] of a collection of exact Lagrangians in a Lionville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from the Hochschild homology of [special characters omitted] to symplectic cohomology and from symplectic cohomology to the Hochschild cohomology of [special characters omitted] 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 [special characters omitted] 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. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Fukaya category; Symplectic cohomology
Title
Symplectic Cohomology and Duality for the Wrapped Fukaya Category
Author
Ganatra, Sheel
Number of pages
0
Degree date
2012
School code
0753
Source
DAI-B 74/04(E), Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
Advisor
Auroux, Denis
Committee member
Auroux, Denis
University/institution
Massachusetts Institute of Technology
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
0828785
ProQuest document ID
1238001248
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/1238001248