Presentation and central extensions of mapping class groups

Abstract

We give a presentation of the mapping class group M \mathcal {M} of a (possibly bounded) surface, considering either all twists or just non-separating twists as generators. We also study certain central extensions of M \mathcal {M} . One of them plays a key role in studying TQFT functors, namely the mapping class group of a p 1 p_1 -structure surface. We give a presentation of this extension.