# A refinement of the Ozsv\'ath-Szab\'o large integer surgery formula and knot concordance

## TL;DR

This paper refines the Ozsváth-Szabó large integer surgery formula, providing a new way to compute knot Floer filtrations for cable knots and relating a knot concordance invariant to filtered maps on Heegaard Floer homology.

## Contribution

It offers a new formula for the knot Floer filtration induced by cable knots in large surgery manifolds, connecting it to the original knot Floer complex and knot concordance invariants.

## Key findings

- Derived a formula for the knot Floer filtration in large surgery manifolds.
- Connected a knot concordance invariant to filtered maps on Heegaard Floer homology.
- Enabled computation of knot invariants via surgery and cable constructions.

## Abstract

We compute the knot Floer filtration induced by a cable of the meridian of a knot in the manifold obtained by large integer surgery along the knot. We give a formula in terms of the original knot Floer complex of the knot in the three-sphere. As an application, we show that a knot concordance invariant of Hom can equivalently be defined in terms of filtered maps on the Heegaard Floer homology groups induced by the two-handle attachment cobordism of surgery along a knot.