Geometry & Topology 12 (2008) 2249–2275

DOI: 10.2140/gt.2008.12.2249

Abstract

By studying the Heegaard Floer homology of the preimage of a knot K ⊂ S³ inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth concordance group. As an application, we prove that all 2–bridge knots of crossing number at most 12 for which the smooth concordance order was previously unknown have infinite smooth concordance order.

Keywords

Smooth knot concordance, Heegaard Floer homology, branched covers, Knot concordance, branched cover, τ–invariant

Mathematical Subject Classification

Primary: 57M25, 57M27, 57R58

Secondary: 57M12, 57M12, 57R58

References

Publication

Received: 1 February 2007
Revised: 24 June 2008
Accepted: 13 June 2008
Published: 2 September 2008
Proposed: Tomasz Mrowka
Seconded: Ronald Stern, Peter Ozsváth

Authors