Embeddings and the (virtual) cohomological dimension of the braid and mapping class groups of surfaces

• DOI: 10.5802/cml.45
• Publication Date: 2018-10-09T14:21:24Z
• Authors: Daciberg Lima Gon...; John Guaschi; Miguel Maldonado
• Keywords: Cohomological dimension; Mapping class group; Braid theory

We use the relations between braid and mapping class groups of a compact, connected, non-orientable surface N without boundary those its orientable double covering S to study embeddings these their (virtual) cohomological dimensions. first generalise results [4, 14] show that group MCG(N;k) relative k-point subset embeds in MCG(S;2k) 2k-point subset. then compute dimension all connected aspherical surfaces boundary, generalising [15]. Finally, if genus is at least 2, we deduce upper bounds for virtual are coherent with computations Ivanov.