A Markov's theorem for extended welded braids and links

TL;DR

This paper extends classical knot theory theorems to the setting of extended welded braids and links, broadening the understanding of their algebraic and topological properties.

Contribution

It establishes Alexander and Markov theorems for extended welded braids and links, generalizing previous results for welded objects.

Findings

Proves Alexander theorem for extended welded links.

Establishes Markov theorem for extended welded braids.

Connects extended welded braids with ribbon and loop braids.

Abstract

Extended welded links are a generalization of Fenn, Rim\'{a}nyi, and Rourke's welded links. Their braided counterpart are extended welded braids, which are closely related to ribbon braids and loop braids. In this paper we prove versions of Alexander and Markov's theorems for extended welded braids and links, following Kamada's approach to the case of welded objects.