Equivariantly Slice Knots in Symmetric 4-Manifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910187604934656 |
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| author | Gabbard, Malcolm |
| author_facet | Gabbard, Malcolm |
| contents | We study the equivariant 4-genus of strongly invertible knots in the $S^3$ boundary of 4-manifolds with involution. We provide techniques for constructing slice disks for knots in various symmetric 4-manifolds via an equivariant version of Marengon and Mihajlovic's tubing construction. Using these techniques, we show that this equivariant 4-genus can differ from the standard 4-genus function of the 4-manifold as well as the equivariant 4-genus of $S^4$. As an example, we show that $S^2\times S^2$ admits an involution such that the figure $8$ knot is equivariantly slice with respect to one of its two strong inversions but not the other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariantly Slice Knots in Symmetric 4-Manifolds Gabbard, Malcolm Geometric Topology 57K10, 57K40, 57R40, 57R42 We study the equivariant 4-genus of strongly invertible knots in the $S^3$ boundary of 4-manifolds with involution. We provide techniques for constructing slice disks for knots in various symmetric 4-manifolds via an equivariant version of Marengon and Mihajlovic's tubing construction. Using these techniques, we show that this equivariant 4-genus can differ from the standard 4-genus function of the 4-manifold as well as the equivariant 4-genus of $S^4$. As an example, we show that $S^2\times S^2$ admits an involution such that the figure $8$ knot is equivariantly slice with respect to one of its two strong inversions but not the other. |
| title | Equivariantly Slice Knots in Symmetric 4-Manifolds |
| topic | Geometric Topology 57K10, 57K40, 57R40, 57R42 |
| url | https://arxiv.org/abs/2605.02006 |