Localization and flexibilization in symplectic geometry
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866911300785799168 |
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| author | Lazarev, Oleg Sylvan, Zachary Tanaka, Hiro Lee |
| author_facet | Lazarev, Oleg Sylvan, Zachary Tanaka, Hiro Lee |
| contents | We introduce the critical Weinstein infinity-category -- the result of stabilizing the category of Weinstein sectors and inverting subcritical morphisms -- and for every finite collection P of integers, construct a P-flexibilization endofunctor. Our main result is that P-flexibilization is an idempotent localization functor of the critical Weinstein infinity-category, allowing us to characterize the essential image of the endofunctor by a universal property. This localization has the effect of replacing every Weinstein sector with one in which P is invertible in the wrapped Fukaya category and hence is a symplectic analogue of topological localization of Bousfield and Sullivan, answering a question of Abouzaid and Seidel. When P = {0}, our construction recovers Cieliebak and Eliashberg's flexibilization procedure. Moreover, we show that P-flexibilization is symmetric monoidal as a functor of higher categories, and hence gives rise to a new way of constructing E-infinity-commutative algebra objects from symplectic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06069 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Localization and flexibilization in symplectic geometry Lazarev, Oleg Sylvan, Zachary Tanaka, Hiro Lee Symplectic Geometry Algebraic Topology We introduce the critical Weinstein infinity-category -- the result of stabilizing the category of Weinstein sectors and inverting subcritical morphisms -- and for every finite collection P of integers, construct a P-flexibilization endofunctor. Our main result is that P-flexibilization is an idempotent localization functor of the critical Weinstein infinity-category, allowing us to characterize the essential image of the endofunctor by a universal property. This localization has the effect of replacing every Weinstein sector with one in which P is invertible in the wrapped Fukaya category and hence is a symplectic analogue of topological localization of Bousfield and Sullivan, answering a question of Abouzaid and Seidel. When P = {0}, our construction recovers Cieliebak and Eliashberg's flexibilization procedure. Moreover, we show that P-flexibilization is symmetric monoidal as a functor of higher categories, and hence gives rise to a new way of constructing E-infinity-commutative algebra objects from symplectic geometry. |
| title | Localization and flexibilization in symplectic geometry |
| topic | Symplectic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2109.06069 |