Palindromic Braids

Abstract

The braid group $B_n$, endowed with Artin's presentation, admits an antiautomorphism $B_n\to B_n$, such that $v\mapsto \bar{v}$ is defined by reading braids in reverse order (from right to left instead of left to right). We prove that the map $B_n\to B_n$, $v\mapsto v\bar{v}$ is injective. We also give some consequences arising due to this injectivity.

8 pages and 1 figure