The signature of a splice

TL;DR

This paper investigates how the signature of colored links behaves under the splice operation, extending the concept to integral homology spheres and revealing an almost additive property with a specific correction term.

Contribution

It extends the signature of colored links to integral homology spheres and provides a closed formula for the correction term in the splice operation.

Findings

Signature is almost additive under splice with a correction term.

Correction term is interpreted as the signature of a generalized Hopf link.

Provides a simple formula to compute the correction term.

Abstract

We study the behavior of the signature of colored links [Flo05, CF08] under the splice operation. We extend the construction to colored links in integral homology spheres and show that the signature is almost additive, with a correction term independent of the links. We interpret this correction term as the signature of a generalized Hopf link and give a simple closed formula to compute it.