THE ALGEBRA OF STRAND SPLITTING II: A PRESENTATION FOR THE BRAID GROUP ON ONE STRAND

Abstract

The author previously introduced groups BV and [Formula: see text] as braided versions of groups introduced by Richard J. Thompson, and as having connections to braided tensor categories. Here we show that BV and [Formula: see text] are finitely presented by exhibiting finite presentations for them. We show that these groups are "Artinifications" of the older Thompson groups V and [Formula: see text] by showing that presentations for V and [Formula: see text] can be obtained from presentations for BV and [Formula: see text] by adding relations that trivialize the squares of the generators of the latter groups.