Knot reversal and rational concordance
Geometric Topology
2022-02-08 v1
Abstract
We give an infinite family of knots that are not rationally concordant to their reverses. More precisely, if R denotes the involution of the rational knot concordance group QC induced by string reversal and Fix(R) denotes the subgroup of knots fixed under R in QC, then QC/Fix(R) contains an infinite rank subgroup. As a corollary, we show that there exists a knot K such that for every pair of coprime integers p and q, the (p,q)-cable of K is not concordant to the reverse of the (p,q)-cable of K.
Keywords
Cite
@article{arxiv.2202.02496,
title = {Knot reversal and rational concordance},
author = {Taehee Kim},
journal= {arXiv preprint arXiv:2202.02496},
year = {2022}
}
Comments
10 pages, 1 figure