Monoid and group of pseudo braids

TL;DR

This paper introduces a monoid of pseudo braids, proves its isomorphism to a singular braid monoid, and establishes an analogue of Markov's theorem for pseudo braids, advancing the algebraic understanding of braid-like structures.

Contribution

It defines a new monoid of pseudo braids and demonstrates its isomorphism to a known singular braid monoid, along with an analogue of Markov's theorem.

Findings

Monoid of pseudo braids is isomorphic to singular braid monoid

Established an analogue of Markov's theorem for pseudo braids

Provides algebraic framework for pseudo braid structures

Abstract

In this paper we define a monoid of pseudo braids and prove that this monoid is isomorphic to a singular braid monoid. We also prove an analogue of Markov's theorem for pseudo braids.