An infinite-rank summand of topologically slice knots

Hom, Jennifer

doi:10.2140/gt.2015.19.1063

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An infinite-rank summand of topologically slice knots

Jennifer Hom

Geometry & Topology 19 (2015) 1063–1110

DOI: 10.2140/gt.2015.19.1063

Correction: 10.2140/gt.2019.23.2699

Abstract

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

Keywords

Heegaaard Floer homology, concordance

Mathematical Subject Classification 2010

Primary: 57N70, 57R58

Secondary: 57M25

References

Publication

Received: 28 October 2013

Revised: 16 May 2014

Accepted: 20 June 2014

Published: 10 April 2015

Proposed: Peter S Ozsváth

Seconded: Cameron Gordon, Tomasz Mrowka

Correction: 13 October 2019

Authors

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

Volume 19, issue 2 (2015)