An infinite-rank summand of topologically slice knots

Hom, Jennifer¹

¹ Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA

Geometry & topology, Tome 19 (2015) no. 2, pp. 1063-1110.

Résumé

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 $\epsilon$.

Détail

DOI : 10.2140/gt.2015.19.1063

Classification : 57N70, 57R58, 57M25
Keywords: Heegaaard Floer homology, concordance

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