# Knot reversal acts non-trivially on the concordance group of topologically slice knots

## TL;DR

This paper constructs an infinite family of topologically slice knots that are not smoothly concordant to their reverses, revealing complex behavior of knot concordance under reversal and expanding understanding of the concordance group.

## Contribution

It demonstrates that the involution induced by string reversal acts non-trivially on the concordance group of topologically slice knots, producing an infinitely generated free subgroup.

## Key findings

- Existence of an infinite family of knots not concordant to their reverses
- The involution acts non-trivially on the concordance group
- Results hold modulo knots with trivial Alexander polynomial

## Abstract

We construct an infinite family of topologically slice knots that are not smoothly concordant to their reverses. More precisely, if T denotes the concordance group of topologically slice knots and R is the involution of T induced by string reversal, then T/Fix(R) contains an infinitely generated free subgroup. The result remains true modulo the subgroup of T generated by knots with trivial Alexander polynomial.