A partial resolution of Hedden's conjecture on satellite homomorphisms

2023/08/14 by Johanningsmeier, Randall, Kim, Hillary, Miller, Allison N.
#57K10 #57M10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2308.06890

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.

Related

• Homomorphism obstructions for satellite maps
• Iterated satellite operators on the knot concordance group
• Some Three and Four-Dimensional Invariants of Satellite Knots with (1,1)-Patterns
• Rank-expanding satellite operators on the topological knot concordance group
• A satellite formula for real Seiberg-Witten Floer homotopy types