FINITE RIGID SETS IN CURVE COMPLEXES

@inproceedings{Aramayona2013FINITERS,
  title={FINITE RIGID SETS IN CURVE COMPLEXES},
  author={Javier Aramayona and Christopher J. Leininger},
  year={2013}
}
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 X → 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 Mod±(S). 

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