Maps from braids to virtual braids and braid representations

TL;DR

This paper leverages virtual knot theory to develop new representations of classical pure braids, highlighting novel features like parity and picture-valued invariants.

Contribution

It introduces a method to construct braid representations using virtual knot theory effects, bridging classical and virtual braid concepts.

Findings

New braid representations derived from virtual knot theory

Enhanced invariants for classical braids using virtual knot features

Connections established between virtual and classical braid theories

Abstract

Virtual knot theory has experienced a lot of nice features that did not appear in classical knot theory, e.g., parity and picture-valued invariants. In the present paper we use virtual knot theory effects to construct new representations of classical (pure) braids.