## Publicacions Matemàtiques

### Automorphism groups of simplicial complexes of infinite-type surfaces

#### Abstract

Let $S$ be an orientable surface of infinite genus with a finite number of boundary components. In this work we consider the curve complex $\mathcal{C}(S)$, the nonseparating curve complex $\mathcal{N}(S)$, and the Schmutz graph $\mathcal{G}(S)$ of $S$. When all topological ends of $S$ carry genus, we show that all elements in the automorphism groups $\operatorname{Aut}(\mathcal{C}(S))$, $\operatorname{Aut}(\mathcal{N}(S))$, and $\operatorname{Aut}(\mathcal{G}(S))$ are geometric, i.e., these groups are naturally isomorphic to the extended mapping class group $\operatorname{MCG}^{*}(S)$ of the infinite surface $S$. Finally, we study rigidity phenomena within $\operatorname{Aut}(\mathcal{C}(S))$ and $\operatorname{Aut}(\mathcal{N}(S))$.

#### Article information

Source
Publ. Mat., Volume 61, Number 1 (2017), 51-82.

Dates
Revised: 4 May 2016
First available in Project Euclid: 22 December 2016

https://projecteuclid.org/euclid.pm/1482375624

Digital Object Identifier
doi:10.5565/PUBLMAT_61117_02

Mathematical Reviews number (MathSciNet)
MR3590114

Zentralblatt MATH identifier
06697025

Subjects