The genus filtration in the smooth concordance group

Shida Wang

Vol. 285 (2016), No. 2, 501–510

DOI: 10.2140/pjm.2016.285.501

Abstract

We define a filtration of the smooth concordance group based on the genus of representative knots. We use the Heegaard Floer $\epsilon$- and $\Upsilon$-invariants to prove the quotient groups with respect to this filtration are infinitely generated. Results are applied to three infinite families of topologically slice knots.

Keywords

knot concordance, genus, Heegaard Floer homology

Mathematical Subject Classification 2010

Primary: 57N70

Secondary: 57M25

Milestones

Received: 26 October 2015

Revised: 23 June 2016

Accepted: 23 June 2016

Published: 21 November 2016