#### Volume 19, issue 2 (2015)

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An infinite-rank summand of topologically slice knots

### Jennifer Hom

Geometry & Topology 19 (2015) 1063–1110
##### Abstract

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

##### Keywords
Heegaaard Floer homology, concordance
##### Mathematical Subject Classification 2010
Primary: 57N70, 57R58
Secondary: 57M25