Crossing-changeable braids from chromatic configuration spaces

TL;DR

This paper introduces a new class of braids derived from chromatic configuration spaces, where strings can intersect and be untangled, extending traditional braid theory.

Contribution

It develops the theory of crossing-changeable braids, a novel concept that generalizes ordinary braids by allowing intersections and untangling within chromatic configuration spaces.

Findings

Defines crossing-changeable braids within chromatic configuration spaces

Shows these braids can have intersecting strings and be untangled

Extends classical braid theory to a broader context

Abstract

Motivated by the work in [15], this paper deals with the theory of the braids from chromatic configuration spaces. This kind of braids possess the property that some strings of each braid may intersect together and can also be untangled, so they are quite different from the ordinary braids in the sense of Artin. This enriches and extends the theory of ordinary braids.