Knot concordance and Heegaard Floer homology invariants in branched covers

2007/01/30 by J. Elisenda Grigsby, J Elisenda Grigsby, Daniel Ruberman +2
Mathematics · #Advanced Combinatorial Mathematics #Concordance #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot invariant #Tricolorability #math.GT #math.SG #msc:57M12 #msc:57M27 #msc:57R58

paper · pdf · doi:10.2140/gt.2008.12.2249

published as Geom. Topol. 12 (2008) 2249-2275 · Expanded references; 25 pages, 5 figures

arxiv created 2007/01/30 · openalex publication_date 2008/09/02 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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

Citations

• An application of gauge theory to four-dimensional topology
• Holomorphic disks and knot invariants
• Sums of lens spaces bounding rational balls
• Knot concordance, Whitney towers and L2-signatures
• On combinatorial link Floer homology
• Lens spaces, rational balls and the ribbon conjecture
• Holomorphic disks and topological invariants for closed three-manifolds