Inverting primes in symplectic geometry

Abstract: A classical construction in topology associates to a space X and prime p, a new "localized" space X_p whose homotopy and homology groups are obtained from those of X by inverting p. In this talk, I will discuss a symplectic analog of this construction and explain how it interpolates between "flexible" and "rigid" symplectic manifolds.

Concretely, I will produce prime-localized Weinstein subdomains of high-dimensional Weinstein domains (which can be thought of as singular Lagrangians) and show that any Weinstein subdomain of a cotangent bundle agrees Fukaya-categorically with one of these special subdomains. The key will be to classify which objects of the Fukaya category of T*M - twisted complexes of Lagrangians - are quasi-isomorphic to actual Lagrangians. This talk is based on joint work with Zach Sylvan and Hiro Lee Tanaka.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

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