Symmetric arcs and homological stability for surfaces

Specialeforsvar ved Alexander Jasper 

Titel: Symmetric arcs and homological stability for surfaces 

Abstract: Many classical sequences of groups $G_n$ induce isomorphisms in group homology from some point depending on the homology degree. We cover a spectral sequence argument involving highly connected simplicial complexes $X_n$ with $G_n$-actions that can be used to establish such results, including tools to show that the simplicial complexes are highly connected. We apply this to the sequence of braid groups and sequences of mapping class groups of surfaces with increasing genus or number of boundary components. Finally we apply it to a sequence of subgroups of mapping class groups of surfaces called symmetric mapping class groups whose elements commute with fixed involutions of the surfaces 

Vejleder: Nathalie Wahl
Censor:   Kasper Klinkby Sonne Andersen, Lunds Universitet