Covariantly functorial wrapped Floer theory on Liouville sectors

Sheel Ganatra; John Pardon; Vivek Shende

doi:10.1007/s10240-019-00112-x

Covariantly functorial wrapped Floer theory on Liouville sectors

Sheel Ganatra
, John Pardon
, Vivek Shende

Mathematics

Research output: Contribution to journal › Article › peer-review

86 Scopus citations

Abstract

We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid’s generation criterion follows.

Original language	English (US)
Pages (from-to)	73-200
Number of pages	128
Journal	Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume	131
Issue number	1
DOIs	https://doi.org/10.1007/s10240-019-00112-x
State	Published - Jun 1 2020

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s10240-019-00112-x

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title = "Covariantly functorial wrapped Floer theory on Liouville sectors",

abstract = "We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid{\textquoteright}s generation criterion follows.",

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AB - We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly functorial with respect to inclusions of Liouville sectors. From this foundational setup, a local-to-global principle for Abouzaid’s generation criterion follows.

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Covariantly functorial wrapped Floer theory on Liouville sectors

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