Finite rigid sets in curve complexes
LEININGER, CHRISTOPHER J.
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ARAMAYONA, JAVIER; LEININGER, CHRISTOPHER J. (2013). Finite rigid sets in curve complexes. Journal of Topology and Analysis 5 (2), 183-203
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 -&gt; C(S) is the restriction of an element of Aut(C(S)), unique up to the (finite) pointwise 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).