A Partial Resolution Of Hedden’s Conjecture On Satellite Homomorphisms

Authors

Randall Johanningsmeier , '24
Hillary Kim , '25
Allison N. Miller, Swarthmore CollegeFollow

Document Type

Article

Publication Date

8-29-2025

Published In

Mathematical Proceedings Of The Cambridge Philosophical Society

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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Comments

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Recommended Citation

Randall Johanningsmeier , '24; Hillary Kim , '25; and Allison N. Miller. (2025). "A Partial Resolution Of Hedden’s Conjecture On Satellite Homomorphisms". Mathematical Proceedings Of The Cambridge Philosophical Society. DOI: 10.1017/S0305004125101485
https://works.swarthmore.edu/fac-math-stat/342