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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.