Embeddings of braid groups into mapping class groups and their homology

2012/04/19 by Bödigheimer, Carl-Friedrich, Tillmann, Ulrike · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1204.4310

Abstract

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.

Cited by

• Liftable braids and the coloured braid groupoid

Related

• Braids, mapping class groups, and categorical delooping
• Geometric representations of the braid group on a nonorientable surface
• The braidings in the mapping class groups of surfaces
• From braid groups to mapping class groups
• Geometric representations of the braid groups