A partial resolution of Hedden's conjecture on satellite homomorphisms

Randall Johanningsmeier; Hillary Kim; Allison N. Miller

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arXiv · 2308.06890

A partial resolution of Hedden's conjecture on satellite homomorphisms

Randall Johanningsmeier·Hillary Kim·Allison N. Miller

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Abstract

A pattern knot in a solid torus defines a self-map of the smooth knot concordance group. We prove that if the winding number of a pattern is even but not divisible by 8, then the corresponding map is not a homomorphism, thus partially establishing a conjecture of Hedden.

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Randall Johanningsmeier, Hillary Kim, Allison N. Miller. 2023-08-14. A partial resolution of Hedden's conjecture on satellite homomorphisms. https://arxiv.org/abs/2308.06890

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