A partial resolution of Hedden’s conjecture on satellite homomorphisms

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.

Authors

Institutions

Publication Details

Journal
Mathematical Proceedings of the Cambridge Philosophical Society
Published
2025-08-29
DOI
https://doi.org/10.1017/s0305004125101485
Primary Topic
Geometric and Algebraic Topology
Type
article
Field-Weighted Citation Impact
0.00

Funders

Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

A partial resolution of Hedden’s conjecture on satellite homomorphisms

Allison N. Miller, Randall Johanningsmeier, Hillary Kim
Mathematical Proceedings of the Cambridge Philosophical Society
Geometric and Algebraic Topology
article

A partial resolution of Hedden’s conjecture on satellite homomorphisms

Allison N. Miller, Randall Johanningsmeier, Hillary Kim
article en

Abstract

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.

Mathematical Proceedings of the Cambridge Philosophical SocietyVol. 180(1)
Swarthmore College (US)
Swarthmore College
Openalex Percentile: Top 72%
Geometric and Algebraic Topology
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

A partial resolution of Hedden’s conjecture on satellite homomorphisms — Allison N. Miller, Randall Johanningsmeier, et al. · Mathematical Proceedings of the Cambridge Philosophical Society (2025) | TGRS Research Map | TGRS