Automorphism groups of simplicial complexes of infinite type surfaces

2014/02/13 by Jesús Hernández Hernández, Hernández, Jesús Hernández, Lorenzo, José Ferrán Valdez
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1402.3275

Abstract

Let S be any orientable surface of infinite genus with a finite 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 the 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))

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