Palindromic Braids

• DOI: 10.4310/ajm.2008.v12.n1.a5
• Publication Date: 2013-08-30T21:54:19Z
• Authors: Florian Deloup; David Garber; Shmuel Kaplan; Mina Teicher
• Keywords: 0301 basic medicine; 11E81; Braid; palindrome; Jacquemard; Garside; Geometric Topology (math.GT); Group Theory (math.GR); Mathematics - Geometric Topology; 03 medical and health sciences; 11E39; FOS: Mathematics; Mathematics - Group Theory

8 pages and 1 figure<br/>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.<br/>