Type: Article

Automorphisms groups of simplicial complexes of infinite-type surfaces

Hernández, J. H; Valdez, F.;

Abstract:

Let S be an orientable surface of infinite genus with a infinite number of boundary components. In this work we consider the curve complex C(S), the nonseparating curve complex N(S), and the Schmutz graph G(S) of S. When all topological ends of S carry genus, we show that all elements in the automorphism groups Aut(C(S)), Aut(N(S)), and Aut(G(S)) are geometric, i.e. these groups are naturally isomorphic to the extended mapping class group MCG ?(S) of the infinite surface S. Finally, we study rigidity phenomena within Aut(C(S)) and Aut(N(S)). 2010 Mathematics Subject Classification: 20F65.