Knot concordance and Heegaard Floer homology invariants in branched covers

Grigsby, J Elisenda¹ ; Ruberman, Daniel² ; Strle, Sašo³

¹ Department of Mathematics, Columbia University, 2990 Broadway MC4406, New York, NY 10027, USA
² Department of Mathematics, MS 050, Brandeis University, Waltham, MA 02454, USA
³ Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 21, 1000 Ljubljana, Slovenia

Geometry & topology, Tome 12 (2008) no. 4, pp. 2249-2275.

Résumé

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.

Détail

DOI : 10.2140/gt.2008.12.2249

Keywords: Smooth knot concordance, Heegaard Floer homology, branched covers, Knot concordance, branched cover, $\tau$–invariant

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