Heegaard Floer homology and concordance bounds on the Thurston norm

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.