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Prime-localized Weinstein subdomains

Oleg Lazarev and Zachary Sylvan

Geometry & Topology 27 (2023) 699–737

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.

symplectic geometry, localization, primes, Weinstein, subdomain, nested
Mathematical Subject Classification
Primary: 53D37, 57R17
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
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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