# Multivariable signatures, genus bounds and $0.5$-solvable cobordisms

## TL;DR

This paper refines bounds on how multivariable signatures and nullities of links change under cobordisms, extending classical inequalities and invariance results to broader contexts, including 0.5-solvable cobordisms.

## Contribution

It generalizes the Murasugi-Tristram inequality and extends invariance of multivariable signatures to 0.5-solvable cobordisms.

## Key findings

- Refined bounds on signature and nullity changes under link cobordisms.
- Extended invariance of multivariable signatures to 0.5-solvable cobordisms.
- Generalized classical inequalities to broader link cobordism contexts.

## Abstract

We refine prior bounds on how the multivariable signature and the nullity of a link change under link cobordisms. The formula generalizes a series of results about the 4-genus having their origins in the Murasugi-Tristram inequality, and at the same time extends previously known results about concordance invariance of the signature to a bigger set of allowed variables. Finally, we show that the multivariable signature and nullity are also invariant under $0.5$-solvable cobordism.