Knot concordance and Heegaard Floer homology invariants in branched covers

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. © 2008 Mathematical Sciences Publishers.