Covariantly functorial wrapped Floer theory on Liouville sectors

2017/06/30 by Sheel Ganatra, John Pardon, Vivek Shende · 3 citations
Mathematics · #math.SG

paper · pdf · doi:10.1007/s10240-019-00112-x

published as Publ. Math. Inst. Hautes Études Sci. 131 (2020), 73-200 · Final version to appear in Publ Math IHES, 115 pages, 15 figures

arxiv created 2019/07/31 · arxiv updated 2020/08/13

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.

Cited by

• Topological algebra of symplectic geometry of symmetric powers
• Density of fibers for the filtered Fukaya category of T^*N
• Splitting symplectic monodromy