# Twisted virtual braids and twisted links

## TL;DR

This paper extends classical knot theory to twisted virtual braids and links, establishing fundamental theorems and algebraic structures that generalize known results to this new context.

## Contribution

It proves Alexander and Markov theorems for twisted virtual links and provides group presentations for the twisted virtual braid group.

## Key findings

- Established Alexander theorem for twisted virtual links
- Proved Markov theorem for twisted virtual links
- Provided group and reduced group presentations for the twisted virtual braid group

## Abstract

Twisted knot theory introduced by M. Bourgoin is a generalization of knot theory. It leads us to the notion of twisted virtual braids. In this paper we show theorems for twisted links corresponding to the Alexander theorem and the Markov theorem in knot theory. We also provide a group presentation and a reduced group presentation of the twisted virtual braid group.