A Rasmussen invariant for links in $\mathbb{RP}^3$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929595899445248 |
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| author | Manolescu, Ciprian Willis, Michael |
| author_facet | Manolescu, Ciprian Willis, Michael |
| contents | Asaeda-Przytycki-Sikora, Manturov, and Gabrovšek extended Khovanov homology to links in $\mathbb{RP}^3$. We construct a Lee-type deformation of their theory, and use it to define an analogue of Rasmussen's s-invariant in this setting. We show that the s-invariant gives constraints on the genera of link cobordisms in the cylinder $I \times \mathbb{RP}^3$. As an application, we give examples of freely 2-periodic knots in $S^3$ that are concordant but not standardly equivariantly concordant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09764 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Rasmussen invariant for links in $\mathbb{RP}^3$ Manolescu, Ciprian Willis, Michael Geometric Topology Quantum Algebra 57K18 (Primary) 57R85 (Secondary) Asaeda-Przytycki-Sikora, Manturov, and Gabrovšek extended Khovanov homology to links in $\mathbb{RP}^3$. We construct a Lee-type deformation of their theory, and use it to define an analogue of Rasmussen's s-invariant in this setting. We show that the s-invariant gives constraints on the genera of link cobordisms in the cylinder $I \times \mathbb{RP}^3$. As an application, we give examples of freely 2-periodic knots in $S^3$ that are concordant but not standardly equivariantly concordant. |
| title | A Rasmussen invariant for links in $\mathbb{RP}^3$ |
| topic | Geometric Topology Quantum Algebra 57K18 (Primary) 57R85 (Secondary) |
| url | https://arxiv.org/abs/2301.09764 |