Knot concordance and Heegaard Floer homology invariants in branched covers

Abstract

By studying the Heegaard Floer homology of the preimage of a knot $K\subset S^3$ 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.