Prime-localized Weinstein subdomains

Lazarev, Oleg¹ ; Sylvan, Zachary²

¹ Department of Mathematics, University of Massachusetts Boston, Boston, MA, United States
² Columbia University, New York, NY, United States

Geometry & topology, Tome 27 (2023) no. 2, pp. 699-737.

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.699

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

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