An odd Khovanov homotopy type
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866912016369713152 |
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| author | Sarkar, Sucharit Scaduto, Christopher Stoffregen, Matthew |
| author_facet | Sarkar, Sucharit Scaduto, Christopher Stoffregen, Matthew |
| contents | For each link L in S^3 and every quantum grading j, we construct a stable homotopy type X^j_o(L) whose cohomology recovers Ozsvath-Rasmussen-Szabo's odd Khovanov homology, H_i(X^j_o(L)) = Kh^{i,j}_o(L), following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable homotopy type. Furthermore, the odd Khovanov homotopy type carries a Z/2 action whose fixed point set is a desuspension of the even Khovanov homotopy type. We also construct a Z/2 action on an even Khovanov homotopy type, with fixed point set a desuspension of X^j_o(L). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_06308 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An odd Khovanov homotopy type Sarkar, Sucharit Scaduto, Christopher Stoffregen, Matthew Geometric Topology For each link L in S^3 and every quantum grading j, we construct a stable homotopy type X^j_o(L) whose cohomology recovers Ozsvath-Rasmussen-Szabo's odd Khovanov homology, H_i(X^j_o(L)) = Kh^{i,j}_o(L), following a construction of Lawson-Lipshitz-Sarkar of the even Khovanov stable homotopy type. Furthermore, the odd Khovanov homotopy type carries a Z/2 action whose fixed point set is a desuspension of the even Khovanov homotopy type. We also construct a Z/2 action on an even Khovanov homotopy type, with fixed point set a desuspension of X^j_o(L). |
| title | An odd Khovanov homotopy type |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/1801.06308 |