Concordance invariants with applications to the 4-dimensional clasp number.

Using knot Floer homology, we define a family of concordance invariants which give lower bounds on the 4-dimensional clasp number. More generally, our invariants obstruct a slice surface with genus $g$ and $c$ double points. We give examples where the clasp number is arbitrarily larger than the 4-ball genus. We also prove that Hendricks and Manolescu's involutive correction terms of large surgery give a lower bound on the clasp number.