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An $L_\infty$ structure on symplectic cohomology

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arxiv 2408.09163 v2 pith:G5DJNYJN submitted 2024-08-17 math.SG

Matthew Strom Borman , Mohamed El Alami , Nick Sheridan This is my paper · ORCID
classification math.SG
keywords symplecticcochainsconstructioninftycohomologyconstructcontrastdomain
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abstract

We construct the $L_\infty$ structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed--open map to an $L_\infty$ homomorphism from symplectic cochains to Hochschild cochains on the wrapped Fukaya category. Features of our construction are that it respects a modified action filtration (in contrast to Pomerleano--Seidel's construction); it uses a compact telescope model (in contrast to Abouzaid--Groman--Varolgunes' construction); and it is adapted to the purposes of our follow-up work where we construct Maurer--Cartan elements in symplectic cochains which are associated to a normal-crossings compactification of the Liouville domain.

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  1. A Deformation of the Compact Fukaya Category via the Relative Fukaya Category

    math.SG 2026-07 accept novelty 6.0 of 10

    The compact subcategory W(M,D) of the CO(β)-deformed wrapped Fukaya category is filtered quasi-equivalent to Seidel's relative Fukaya category F(M,D).

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