Finite presentations for spherical/braid twist groups from decorated marked surfaces

Abstract

We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the associated 3-Calabi-Yau triangulated category. The motivation/application is that the result will be used to show that the (principal component of) space of stability conditions on the 3-Calabi-Yau category is simply connected in the sequel.