Concordance surgery and the Ozsv\'ath-Szab\'o 4-manifold invariant

TL;DR

This paper derives a formula for how concordance surgery affects the Ozsváth-Szabó 4-manifold invariant, linking it to the graded Lefschetz number of a knot Floer homology map, using sutured Floer TQFT techniques.

Contribution

It introduces a new formula connecting concordance surgery effects to knot Floer homology invariants, expanding understanding of 4-manifold invariants.

Findings

Derived a formula involving the graded Lefschetz number of the concordance map.

Applied sutured Floer TQFT and perturbed sutured Floer homology in the proof.

Enhanced the computational tools for 4-manifold invariants under concordance surgery.

Abstract

We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsv\'ath-Szab\'o 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.