Inverting primes in Weinstein geometry

Oleg Lazarev

A classical construction in topology associates to a space X and prime p, a new "localized" space Xp 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, extending work of Abouzaid-Seidel and Cieliebak-Eliashberg on flexible Weinstein structures. Concretely, I will produce prime-localized Weinstein subdomains of high-dimensional Weinstein domains and also 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 Z. Sylvan.

https://www.ias.edu/video/inverting-primes-weinstein-geometry