On virtual cabling and structure of 4-strand virtual pure braid group

Abstract

This article is dedicate to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group $V{P}_n$. Consequently we describe $V{P}_4$ as HNN-extension. As an application to classical braids, we find a new presentation of the Artin pure braid group $P_4$ in terms of the cabled generators.

29 pages, 1 figure

Cited by in corpus (1)

• Lifting theorem for the virtual pure braid groups