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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
An infinite-rank summand of topologically slice knots

Jennifer Hom

Geometry & Topology 19 (2015) 1063–1110
Abstract

Let CTS be the subgroup of the smooth knot concordance group generated by topologically slice knots. Endo showed that CTS contains an infinite-rank subgroup, and Livingston and Manolescu-Owens showed that CTS contains a 3 summand. We show that in fact CTS contains a 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
Authors
Jennifer Hom
Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027
USA