Knot concordance and Heegaard Floer homology invariants in branched covers

Details Knot concordance and Heegaard Floer homology invariants in branched covers Knot concordance and Heegaard Floer homology invariants in branched covers

2007-01-16

arxiv.org/abs/math/0701460v2

Mathematics

Geometric Topology

Expanded references; 25 pages, 5 figures

Scientific paper

By studying the Heegaard Floer homology of the preimage of a knot K in 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.

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