Smooth concordance of cables of the figure-eight knot
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909602745942016 |
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| author | Kang, Sungkyung Park, JungHwan Taniguchi, Masaki |
| author_facet | Kang, Sungkyung Park, JungHwan Taniguchi, Masaki |
| contents | We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all $(2n,1)$-cables of the figure-eight knot. To this end, we introduce a family of concordance invariants $κ_R^{(k)}$, defined via $2^k$-fold branched covers and real Seiberg--Witten Floer $K$-theory. These invariants generalize the real $K$-theoretic Frøyshov invariant developed by Konno, Miyazawa, and Taniguchi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Smooth concordance of cables of the figure-eight knot Kang, Sungkyung Park, JungHwan Taniguchi, Masaki Geometric Topology 57K10, 57K41 We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all $(2n,1)$-cables of the figure-eight knot. To this end, we introduce a family of concordance invariants $κ_R^{(k)}$, defined via $2^k$-fold branched covers and real Seiberg--Witten Floer $K$-theory. These invariants generalize the real $K$-theoretic Frøyshov invariant developed by Konno, Miyazawa, and Taniguchi. |
| title | Smooth concordance of cables of the figure-eight knot |
| topic | Geometric Topology 57K10, 57K41 |
| url | https://arxiv.org/abs/2505.03720 |