# Localization and flexibilization in symplectic geometry

@inproceedings{Lazarev2021LocalizationAF, title={Localization and flexibilization in symplectic geometry}, author={Oleg Lazarev and Zachary Sylvan and Hirokazu Tanaka}, year={2021} }

We introduce the critical Weinstein category the result of stabilizing the category of Weinstein sectors and inverting subcritical morphisms and construct localizing ‘P-flexibilization’ endofunctors indexed by collections P of Lagrangian disks in the stabilization of a point T ∗D0. Like the classical localization of topological spaces studied by Quillen, Sullivan, and others, these functors are homotopy-invariant and localizing on algebraic invariants like the Fukaya category. Furthermore…

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