Publicacions Matemàtiques

Automorphism groups of simplicial complexes of infinite-type surfaces

Jesús Hernández Hernández and Ferrán Valdez

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Curve complex infinite type surface


Hernández, Jesús Hernández; Valdez, Ferrán. Automorphism groups of simplicial complexes of infinite-type surfaces. Publ. Mat. 61 (2017), no. 1, 51--82. doi:10.5565/PUBLMAT_61117_02.

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