Prime-localized Weinstein subdomains

Lazarev, Oleg; Sylvan, Zachary

doi:10.2140/gt.2023.27.699

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Prime-localized Weinstein subdomains

Oleg Lazarev and Zachary Sylvan

Geometry & Topology 27 (2023) 699–737

DOI: 10.2140/gt.2023.27.699

Abstract

For any high-dimensional Weinstein domain and finite collection of primes, we construct a Weinstein subdomain whose wrapped Fukaya category is a localization of the original wrapped Fukaya category away from the given primes. When the original domain is a cotangent bundle, these subdomains form a decreasing lattice whose order cannot be reversed.

Furthermore, we classify the possible wrapped Fukaya categories of Weinstein subdomains of a cotangent bundle of a simply connected, spin manifold, showing that they all coincide with one of these prime localizations. In the process, we describe which twisted complexes in the wrapped Fukaya category of a cotangent bundle of a sphere are isomorphic to genuine Lagrangians.

Keywords

symplectic geometry, localization, primes, Weinstein, subdomain, nested

Mathematical Subject Classification

Primary: 53D37, 57R17

References

Publication

Received: 6 October 2020

Revised: 12 August 2021

Accepted: 16 October 2021

Published: 16 May 2023

Proposed: Leonid Polterovich

Seconded: Paul Seidel, András I Stipsicz

Authors

Oleg Lazarev
Department of Mathematics University of Massachusetts Boston Boston, MA United States

Zachary Sylvan
Columbia University New York, NY United States

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Volume 27, issue 2 (2023)