Localization and flexibilization in symplectic geometry
Abstract
We introduce the critical Weinstein category  the result of stabilizing the category of Weinstein sectors and inverting subcritical morphisms  and construct localizing `Pflexibilization' endofunctors indexed by collections $P$ of Lagrangian disks in the stabilization of a point $T^*D^0$. Like the classical localization of topological spaces studied by Quillen, Sullivan, and others, these functors are homotopyinvariant and localizing on algebraic invariants like the Fukaya category. Furthermore, these functors generalize the `flexibilization' operation introduced by CieliebakEliashberg and Murphy and the `homologous recombination' construction of AbouzaidSeidel. In particular, we give an hprinciplefree proof that flexibilization is idempotent and independent of presentation, up to subcriticals and stabilization. In fact, we show that $P$flexibilization is a multiplicative localization of the critical Weinstein category, and hence gives rise to a new way of constructing commutative algebra objects from symplectic geometry.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.06069
 Bibcode:
 2021arXiv210906069L
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Algebraic Topology
 EPrint:
 Comments welcome!