Heegaard Floer homology and concordance bounds on the Thurston norm

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 $S^3$. We then specialise this procedure to knots in $S^2\times S^1$, and obtain a lower bound on their geometric winding number. Furthermore we produce an obstruction for a knot in $S^3$ 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.

With an appendix with Adam Simon Levine; 24 pages, 8 figures; comments welcome! V2: Fixed a few typos, wrong citations and figures, removed a proposition. This version to appear in Transactions of the AMS