Global rigidity of solvable group actions on S1

Lizzie Burslem*, Amie Wilkinson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


In this paper we find all solvable subgroups of Diff ω(S1) and classify their actions. We also investigate the Cr local rigidity of actions of the solvable Baumslag-Solitar groups on the circle. The investigation leads to two novel phenomena in the study of infinite group actions on compact manifolds. We exhibit a finitely generated group Γ and a manifold M such that: • has exactly countably innitely many effective real-analytic actions on M, up to conjugacy in Diffω(M); • every effective, real analytic action of Γ on M is Cr locally rigid, for some r ≥ 3, and for every such r, there are infinitely many nonconjugate, effective real-analytic actions of Γ on M that are Cr locally rigid, but not Cr-1 locally rigid.

Original languageEnglish (US)
Pages (from-to)877-924
Number of pages48
JournalGeometry and Topology
StatePublished - 2004


  • Diff(S)
  • Group action
  • Rigidity
  • Solvable group

ASJC Scopus subject areas

  • Geometry and Topology


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