Twisted right-angled Artin groups embedded in knot groups

TL;DR

This paper characterizes which twisted right-angled Artin groups, defined via mixed graphs with specific relations, can be embedded into knot groups, extending the understanding of their algebraic and topological relationships.

Contribution

It provides a complete characterization of twisted right-angled Artin groups that can be embedded in knot groups, generalizing previous results on right-angled Artin groups.

Findings

Complete characterization of embeddable twisted right-angled Artin groups

Extension of Katayama's work on right-angled Artin groups

New insights into the algebraic structure of knot groups

Abstract

Twisted right-angled Artin groups are defined through presentation based on mixed graphs. Each vertex corresponds to a generator, each undirected edge yields a commuting relation and each directed edge gives a Klein bottle relation. If there is no directed edge, then this reduces to an ordinary right-angled Artin group. There is a characterization of right-angled Artin groups which can be embedded in knot groups by Katayama. In this paper, we completely determine twisted right-angled Artin groups embedded in knot groups.