Heegaard Floer homology and concordance bounds on the Thurston norm

2018/06/27 by Celoria, Daniele, Golla, Marco
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1806.10562

Abstract

We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a 2-component link L in S³. We then specialise this procedure to knots in S²× S¹, and obtain a lower bound on their geometric winding number. Furthermore we produce an obstruction for a knot in S³ to have untwisting number 1. We then provide an infinite family of null-homologous knots with increasing geometric winding number, on which the bound is sharp.

Related

• Order in the concordance group and Heegaard Floer homology
• Heegaard diagrams and Floer homology
• Knot Floer homology and relative adjunction inequalities
• Correction terms, \mathbb Z₂--Thurston norm, and triangulations
• Link Floer homology and the Thurston norm