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Finite rigid sets in curve complexes

ARAMAYONA, JAVIER
; 
LEININGER, CHRISTOPHER J.
Repository DOI
Publication Date
2013-06-01
Keywords
surfaces, curve complex, mapping class group, mapping class-groups, automorphisms
Type
Article
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Citation
ARAMAYONA, JAVIER; LEININGER, CHRISTOPHER J. (2013). Finite rigid sets in curve complexes. Journal of Topology and Analysis 5 (2), 183-203
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 X -> 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).
Funder
Publisher
World Scientific Pub Co Pte Lt
Publisher DOI
10.1142/s1793525313500076
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)