The symplectic arc algebra is formal
We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degree-one Hochschild cohomology class on a Floer A$_\infty$-algebra associated to the ($k$,$k$...
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| Autori principali: | , |
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| Lingua: | inglese |
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Duke University Press
2019
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| Accesso online: | https://demo7.dspace.org/handle/123456789/469 |
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| _version_ | 1860822453960310784 |
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| author | Abouzaid, Mohammed Smith, Ivan |
| author_browse | Abouzaid, Mohammed Smith, Ivan |
| author_facet | Abouzaid, Mohammed Smith, Ivan |
| author_sort | Abouzaid, Mohammed |
| collection | DSpace |
| description | We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degree-one Hochschild cohomology class on a Floer A$_\infty$-algebra associated to the ($k$,$k$)-nilpotent slice $y_k$ obtained by counting holomorphic discs which satisfy a suitable conormal condition at infinity in a partial compactification $\bar y$$_k$. The space $\bar y$$_k$ is obtained as the Hilbert scheme of a partial compactification of the A$_{2k-1}$-Milnor fiber. A sequel to this paper will prove formality of the symplectic cup and cap bimodules and infer that symplectic Khovanov cohomology and Khovanov cohomology have the same total rank over characteristic zero fields. |
| id | oai:localhost:123456789-469 |
| institution | DSPACE.FCHPT |
| language | English |
| publishDate | 2019 |
| publishDateRange | 2019 |
| publishDateSort | 2019 |
| publisher | Duke University Press |
| publisherStr | Duke University Press |
| record_format | dspace |
| spelling | oai:localhost:123456789-4692021-04-07T16:30:12Z The symplectic arc algebra is formal Abouzaid, Mohammed Smith, Ivan We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degree-one Hochschild cohomology class on a Floer A$_\infty$-algebra associated to the ($k$,$k$)-nilpotent slice $y_k$ obtained by counting holomorphic discs which satisfy a suitable conormal condition at infinity in a partial compactification $\bar y$$_k$. The space $\bar y$$_k$ is obtained as the Hilbert scheme of a partial compactification of the A$_{2k-1}$-Milnor fiber. A sequel to this paper will prove formality of the symplectic cup and cap bimodules and infer that symplectic Khovanov cohomology and Khovanov cohomology have the same total rank over characteristic zero fields. 2019-04-26T08:57:22Z 2019-04-26T08:57:22Z 28/01/16 https://demo7.dspace.org/handle/123456789/469 en Duke University Press |
| spellingShingle | Abouzaid, Mohammed Smith, Ivan The symplectic arc algebra is formal |
| title | The symplectic arc algebra is formal |
| title_full | The symplectic arc algebra is formal |
| title_fullStr | The symplectic arc algebra is formal |
| title_full_unstemmed | The symplectic arc algebra is formal |
| title_short | The symplectic arc algebra is formal |
| title_sort | symplectic arc algebra is formal |
| url | https://demo7.dspace.org/handle/123456789/469 |
| work_keys_str_mv | AT abouzaidmohammed thesymplecticarcalgebraisformal AT smithivan thesymplecticarcalgebraisformal AT abouzaidmohammed symplecticarcalgebraisformal AT smithivan symplecticarcalgebraisformal |