ETD

• braid
• homology
• mapping class group
• twisted coefficients

There are several natural ways to embed (i.e. to include as a subgroup) the braid groups into the mapping class groups of surfaces. In this thesis I will study some of these embeddings, and prove that, in most cases, they induce stably the trivial map in homology with symplectic coefficients. This is a generalisation of the stable triviality result that holds for homology with constant coefficients.