The link surgery formula and equivariant surgeries

TL;DR

This paper extends the Heegaard Floer link surgery formula to an equivariant setting, providing new tools for studying equivariant knots and their cobordism groups.

Contribution

It introduces an equivariant version of the Heegaard Floer link surgery formula and applies it to analyze the structure of equivariant homology cobordism groups.

Findings

Established an equivariant knot surgery formula in $S^3$

Proved the kernel of the forgetful map contains a $ ext{Z}^ ext{infty}$-summand

Demonstrated naturality for bordered modules in the equivariant context

Abstract

We prove an equivariant version of the Heegaard Floer link surgery formula. As a special case, this gives an equivariant knot surgery formula for equivariant knots in $S^3$. Our proof goes by way of a naturality theorem for certain bordered modules described by the last author. As a sample application, we prove the kernel of the forgetful map from the equivariant homology cobordism group to the homology cobordism group contains a $\Z^\infty$-summand.