An $L_\infty$ structure on symplectic cohomology
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913579618271232 |
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| author | Borman, Matthew Strom Alami, Mohamed El Sheridan, Nick |
| author_facet | Borman, Matthew Strom Alami, Mohamed El Sheridan, Nick |
| contents | We construct the $L_\infty$ structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed--open map to an $L_\infty$ homomorphism from symplectic cochains to Hochschild cochains on the wrapped Fukaya category. Features of our construction are that it respects a modified action filtration (in contrast to Pomerleano--Seidel's construction); it uses a compact telescope model (in contrast to Abouzaid--Groman--Varolgunes' construction); and it is adapted to the purposes of our follow-up work where we construct Maurer--Cartan elements in symplectic cochains which are associated to a normal-crossings compactification of the Liouville domain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_09163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An $L_\infty$ structure on symplectic cohomology Borman, Matthew Strom Alami, Mohamed El Sheridan, Nick Symplectic Geometry 53D40 We construct the $L_\infty$ structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed--open map to an $L_\infty$ homomorphism from symplectic cochains to Hochschild cochains on the wrapped Fukaya category. Features of our construction are that it respects a modified action filtration (in contrast to Pomerleano--Seidel's construction); it uses a compact telescope model (in contrast to Abouzaid--Groman--Varolgunes' construction); and it is adapted to the purposes of our follow-up work where we construct Maurer--Cartan elements in symplectic cochains which are associated to a normal-crossings compactification of the Liouville domain. |
| title | An $L_\infty$ structure on symplectic cohomology |
| topic | Symplectic Geometry 53D40 |
| url | https://arxiv.org/abs/2408.09163 |