Two second Steenrod squares for odd Khovanov homology
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914070739812352 |
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| author | Schuetz, Dirk |
| author_facet | Schuetz, Dirk |
| contents | Recently, Sarkar-Scaduto-Stoffregen constructed a stable homotopy type for odd Khovanov homology, hence obtaining an action of the Steenrod algebra on Khovanov homology with $\mathbb{Z}/2\mathbb{Z}$ coefficients. Motivated by their construction we propose a way to compute the second Steenrod square. Our construction is not unique, but we can show it to be a link invariant which gives rise to a refinement of the Rasmussen $s$-invariant with $\mathbb{Z}/2\mathbb{Z}$ coefficients. We expect it to be related to the second Steenrod square arising from the Sarkar-Scaduto-Stoffregen construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_00389 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Two second Steenrod squares for odd Khovanov homology Schuetz, Dirk Geometric Topology Algebraic Topology 58K18, 58K10 Recently, Sarkar-Scaduto-Stoffregen constructed a stable homotopy type for odd Khovanov homology, hence obtaining an action of the Steenrod algebra on Khovanov homology with $\mathbb{Z}/2\mathbb{Z}$ coefficients. Motivated by their construction we propose a way to compute the second Steenrod square. Our construction is not unique, but we can show it to be a link invariant which gives rise to a refinement of the Rasmussen $s$-invariant with $\mathbb{Z}/2\mathbb{Z}$ coefficients. We expect it to be related to the second Steenrod square arising from the Sarkar-Scaduto-Stoffregen construction. |
| title | Two second Steenrod squares for odd Khovanov homology |
| topic | Geometric Topology Algebraic Topology 58K18, 58K10 |
| url | https://arxiv.org/abs/2209.00389 |