Explicit Presentations for Exceptional Braid Groups

Abstract

We give presentations for the braid groups associated with the complex reflection groups $G_{24}$ and $G_{27}$. For the cases of $G_{29}$, $G_{31}$, $G_{33}$, and $G_{34}$, we give (strongly supported) conjectures. These presentations were obtained with VKCURVE, a GAP package implementing Van Kampen's method.