Inverting primes in Weinstein geometry

Inverting primes in Weinstein geometry

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Oleg Lazarev, Harvard University

Zoom link:  :  https://theias.zoom.us/j/97116147750?pwd=L2Fud1Y4Z2xsT3dhU2NrV0ZXd3lUQT09

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, 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^{\ast} M – twisted complexes of Lagrangians – are quasi-isomorphic to actual Lagrangians.

This talk is based on joint work with Z. Sylvan.