Finite rigid sets in curve complexes

Javier Aramayona, Christopher J. Leininger

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Pages (from-to)183-203
Number of pages21
JournalJournal of Topology and Analysis
Issue number2
StatePublished - Jun 2013


  • Surfaces
  • curve complex
  • mapping class group

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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