Some remarks on twin groups

Abstract

The twin group $T_n$ is a right angled Coxeter group generated by $n-1$ involutions and having only far commutativity relations. These groups can be thought of as planar analogues of Artin braid groups. In this note, we study some properties of twin groups whose analogues are well-known for Artin braid groups. We give an algorithm for two twins to be equivalent under individual Markov moves. Further, we show that twin groups $T_n$ have $R_{\infty }$-property and are not co-Hopfian for $n\ge 3$.

11 pages, 5 figures

Cited by in corpus (5)

• Structure and automorphisms of pure virtual twin groups
• Automorphisms of odd Coxeter groups
• Congruence subgroups and crystallographic quotients of small Coxeter groups
• Virtual planar braid groups and permutations
• Flat braid groups, right-angled Artin groups, and commensurability