Knot concordance and Heegaard Floer homology invariants in branched covers

Abstract

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.

Expanded references; 25 pages, 5 figures

References in corpus (3)

• Lens spaces, rational balls and the ribbon conjecture
• On combinatorial link Floer homology
• Sums of lens spaces bounding rational balls

Cited by in corpus (8)

• Filtering smooth concordance classes of topologically slice knots
• Heegaard Floer homology and genus one, one boundary component open books
• Obstructions to Lagrangian Cobordisms between Legendrians via Generating Families
• Distinguishing topologically and smoothly doubly slice knots
• Satellites of Infinite Rank in the Smooth Concordance Group
• Equivariant Seiberg-Witten-Floer cohomology
• The concordance genus of a knot, II
• Concordance to links with unknotted components