An infinite-rank summand of topologically slice knots

Abstract

Let ${\mathcal{C}}_{TS}$ be the subgroup of the smooth knot concordance group generated by topologically slice knots. Endo showed that ${\mathcal{C}}_{TS}$ contains an infinite-rank subgroup, and Livingston and Manolescu-Owens showed that ${\mathcal{C}}_{TS}$ contains a ${\mathbb{Z}}^3$ summand. We show that in fact ${\mathcal{C}}_{TS}$ contains a ${\mathbb{Z}}^{\infty }$ summand. The proof relies on the knot Floer homology package of Ozsváth–Szabó and the concordance invariant $\epsilon$.