Involutions, knots, and Floer K-theory
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866908761764921344 |
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| author | Konno, Hokuto Miyazawa, Jin Taniguchi, Masaki |
| author_facet | Konno, Hokuto Miyazawa, Jin Taniguchi, Masaki |
| contents | We establish a version of Seiberg--Witten Floer $K$-theory for knots, as well as a version of Seiberg-Witten Floer $K$-theory for 3-manifolds with involution. The main theorems are 10/8-type inequalities for knots and for involutions. The 10/8-inequality for knots yields numerous applications to knots, such as lower bounds on stabilizing numbers and relative genera. We also give obstructions to extending involutions on 3-manifolds to 4-manifolds, and detect non-smoothable involutions on 4-manifolds with boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_09258 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Involutions, knots, and Floer K-theory Konno, Hokuto Miyazawa, Jin Taniguchi, Masaki Geometric Topology Algebraic Topology Differential Geometry We establish a version of Seiberg--Witten Floer $K$-theory for knots, as well as a version of Seiberg-Witten Floer $K$-theory for 3-manifolds with involution. The main theorems are 10/8-type inequalities for knots and for involutions. The 10/8-inequality for knots yields numerous applications to knots, such as lower bounds on stabilizing numbers and relative genera. We also give obstructions to extending involutions on 3-manifolds to 4-manifolds, and detect non-smoothable involutions on 4-manifolds with boundary. |
| title | Involutions, knots, and Floer K-theory |
| topic | Geometric Topology Algebraic Topology Differential Geometry |
| url | https://arxiv.org/abs/2110.09258 |