A REFINEMENT OF THE OZSVATH-SZABO LARGE INTEGER SURGERY FORMULA AND KNOT CONCORDANCE

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.

Automated summary

We calculate 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. Furthermore, we show that a knot concordance invariant of Hom can be alternatively defined in terms of filtered maps on the Heegaard Floer homology groups induced by the two-handle attachment cobordism of surgery along a knot.