Automorphism groups of simplicial complexes of infinite type surfaces

Jesús Hernández Hernández; José Ferrán Valdez Lorenzo

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arXiv · 1402.3275

Automorphism groups of simplicial complexes of infinite type surfaces

Jesús Hernández Hernández·José Ferrán Valdez Lorenzo

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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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BibTeX RIS

Jesús Hernández Hernández, José Ferrán Valdez Lorenzo. 2014-02-13. Automorphism groups of simplicial complexes of infinite type surfaces. https://arxiv.org/abs/1402.3275

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