Finite rigid sets in curve complexes

Javier Aramayona; Christopher J. Leininger

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arXiv · 1206.3114

Finite rigid sets in curve complexes

Javier Aramayona·Christopher J. Leininger

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Abstract

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S) such that every locally injective simplicial map from X into C(S) is the restriction of an element of Aut(C(S)), unique up to the (finite) point-wise stabilizer of X in Aut(C(S)). Furthermore, if S is not a twice-punctured torus, then we can replace Aut(C(S)) in this statement with the extended mapping class group.

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BibTeX RIS

Javier Aramayona, Christopher J. Leininger. 2012-07-24. Finite rigid sets in curve complexes. https://arxiv.org/abs/1206.3114

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