Palindromic Braids

. The braid group B n , endowed with Artin’s presentation, admits an antiautomorphism B n → B n , such that v 7→ 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 → B n , v 7→ vv is injective. We also give some consequences arising due to this injectivity.