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G&T Monographs |
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Knot concordance and Heegaard Floer homology invariants in
branched covers
J Elisenda Grigsby, Daniel Ruberman and Sašo
Strle
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Geometry & Topology 12 (2008)
2249–2275
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Abstract
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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.
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Keywords
Smooth knot concordance, Heegaard Floer
homology, branched covers, Knot concordance, branched cover,
τ–invariant
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Mathematical Subject Classification
Primary: 57M25, 57M27, 57R58
Secondary: 57M12, 57M12, 57R58
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Publication
Received: 1 February 2007
Revised: 24 June 2008
Accepted: 13 June 2008
Published: 2 September 2008
Proposed: Tomasz Mrowka
Seconded: Ronald Stern, Peter Ozsváth
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