Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929482800037888 |
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| author | Baraglia, David |
| author_facet | Baraglia, David |
| contents | We construct a new family of knot concordance invariants $θ^{(q)}(K)$, where $q$ is a prime number. Our invariants are obtained from the equivariant Seiberg-Witten-Floer cohomology, constructed by the author and Hekmati, applied to the degree $q$ cyclic cover of $S^3$ branched over $K$. In the case $q=2$, our invariant $θ^{(2)}(K)$ shares many similarities with the knot Floer homology invariant $ν^+(K)$ defined by Hom and Wu. Our invariants $θ^{(q)}(K)$ give lower bounds on the genus of any smooth, properly embedded, homologically trivial surface bounding $K$ in a definite $4$-manifold with boundary $S^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11670 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds Baraglia, David Geometric Topology Differential Geometry 57K10, 57K41 We construct a new family of knot concordance invariants $θ^{(q)}(K)$, where $q$ is a prime number. Our invariants are obtained from the equivariant Seiberg-Witten-Floer cohomology, constructed by the author and Hekmati, applied to the degree $q$ cyclic cover of $S^3$ branched over $K$. In the case $q=2$, our invariant $θ^{(2)}(K)$ shares many similarities with the knot Floer homology invariant $ν^+(K)$ defined by Hom and Wu. Our invariants $θ^{(q)}(K)$ give lower bounds on the genus of any smooth, properly embedded, homologically trivial surface bounding $K$ in a definite $4$-manifold with boundary $S^3$. |
| title | Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds |
| topic | Geometric Topology Differential Geometry 57K10, 57K41 |
| url | https://arxiv.org/abs/2205.11670 |