Prime-localized Weinstein subdomains

TL;DR

This paper constructs Weinstein subdomains with wrapped Fukaya categories localized at specified primes, providing a classification for cotangent bundles of simply connected, spin manifolds and analyzing their Lagrangian structures.

Contribution

It introduces a method to create prime-localized Weinstein subdomains and classifies their wrapped Fukaya categories for certain cotangent bundles.

Findings

Constructed Weinstein subdomains with localized wrapped Fukaya categories.

Established a decreasing lattice of subdomains in cotangent bundles.

Identified which twisted complexes correspond to genuine Lagrangians.

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.