Concordance surgery and the Ozsváth-Szabó 4-manifold invariant

Abstract

We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsváth-Szabó 4-manifold invariant. The formula involves the graded Lefschetz number of the concordance map on knot Floer homology. The proof uses the sutured Floer TQFT, and a version of sutured Floer homology perturbed by a 2-form.

37 pages, 4 figures, v2: expanded, new section on naturality of perturbed SFH, v3: improved exposition, to appear in the Journal of the European Mathematical Society