Embeddings of braid groups into mapping class groups and their homology

Carl-Friedrich Bödigheimer, Ulrike Tillmann

Published 2012-04-19Version 1

We construct several families of embeddings of braid groups into mapping class groups of orientable and non-orientable surfaces and prove that they induce the trivial map in stable homology in the orientable case, but not so in the non-orientable case. We show that these embeddings are non-geometric in the sense that the standard generators of the braid group are not mapped to Dehn twists.