Coloring invariants for links in $\Sigma_g\times S^1$

TL;DR

This paper develops coloring invariants for links in the three-dimensional manifold formed by the product of a closed surface of genus g and a circle, providing new tools for link classification in this setting.

Contribution

It introduces a method to define and generalize coloring invariants for links in a extsubscript{g} imes S^1, extending link invariants to this class of 3-manifolds.

Findings

Defined coloring invariants for links in a extsubscript{g} imes S^1

Generalized coloring invariants to broader classes of links

Provided a framework for link classification in a extsubscript{g} imes S^1

Abstract

Let $\Sigma_g$ be a closed oriented surface of genus $g$, in this paper we discuss how to define coloring invariants and its generalizations for links in $\Sigma_g\times S^1$.