Knot reversal and mutation act non-trivially on the concordance group of topologically slice knots

Charles Livingston

Published 2019-04-26Version 1

We construct a topologically slice knot that is not smoothly concordant to its reverse. Moreover, we show that string reversal induces a nontrivial involution on the quotient of the concordance group of topologically slice knots modulo the subgroup generated by knots of Alexander polynomial one. This implies that Conway mutation acts non-trivially on these concordance groups.