Topologically slice knots of smooth concordance order two

Abstract

The existence of topologically slice knots that are of infinite order in the knot concordance group followed from Freedman’s work on topological surgery and Donaldson’s gauge theoretic approach to four-manifolds. Here, as an application of Ozsváth and Szabó’s Heegaard Floer theory, we show the existence of an infinite subgroup of the smooth concordance group generated by topologically slice knots of concordance order two. In addition, no nontrivial element in this subgroup can be represented by a knot with Alexander polynomial one.