#### Volume 12, issue 4 (2008)

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Knot concordance and Heegaard Floer homology invariants in branched covers

### J Elisenda Grigsby, Daniel Ruberman and Sašo Strle

Geometry & Topology 12 (2008) 2249–2275
##### 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.

##### Keywords
Smooth knot concordance, Heegaard Floer homology, branched covers, Knot concordance, branched cover, $\tau$–invariant
##### Mathematical Subject Classification 2000
Primary: 57R58, 57M25
Secondary: 57M12, 57M27