Equivariantly Slice Knots in Symmetric 4-Manifolds

Malcolm Gabbard

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arXiv · 2605.02006

Equivariantly Slice Knots in Symmetric 4-Manifolds

Malcolm Gabbard

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Abstract

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 Mihajlovi\`c'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.

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BibTeX RIS

Malcolm Gabbard. 2026-05-03. Equivariantly Slice Knots in Symmetric 4-Manifolds. https://arxiv.org/abs/2605.02006

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