Open Access
2017 Automorphism groups of simplicial complexes of infinite-type surfaces
Jesús Hernández Hernández, Ferrán Valdez
Publ. Mat. 61(1): 51-82 (2017). DOI: 10.5565/PUBLMAT_61117_02


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 $\operatorname{Aut}(\mathcal{N}(S))$.


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Jesús Hernández Hernández. Ferrán Valdez. "Automorphism groups of simplicial complexes of infinite-type surfaces." Publ. Mat. 61 (1) 51 - 82, 2017.


Received: 2 February 2015; Revised: 4 May 2016; Published: 2017
First available in Project Euclid: 22 December 2016

zbMATH: 06697025
MathSciNet: MR3590114
Digital Object Identifier: 10.5565/PUBLMAT_61117_02

Primary: 20F65

Keywords: curve complex , infinite type surface

Rights: Copyright © 2017 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.61 • No. 1 • 2017
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