On biquandles for the groups $G_n^k$ and surface singular braid monoid

TL;DR

This paper explores biquandle structures on groups $G_n^k$ and constructs a homomorphism from the surface singular braid monoid to $G_n^2$, advancing algebraic tools for dynamical systems and braid theory.

Contribution

It introduces a biquandle structure on $G_n^k$ groups and establishes a homomorphism from the surface singular braid monoid to $G_n^2$, linking braid theory with these groups.

Findings

Biquandle structure defined on $G_n^k$ groups.

Homomorphism constructed from surface singular braid monoid to $G_n^2$.

Provides new algebraic tools for studying dynamical systems and braids.

Abstract

The groups $G_n^k$ were defined by V. O. Manturov in order to describe dynamical systems in configuration systems. In the paper we consider two applications of this theory: we define a biquandle structure on the groups $G_n^k$, and construct a homomorphism from the surface singular braid monoid to the group $G_n^2$.