Groups of homeomorphisms of one-manifolds III: Nilpotent subgroups

Benson Farb*, John Franks

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


This self-contained paper is part of a series (Groups of homeomorphisms of one-manifolds I: actions of nonlinear groups. Preprint, 2001; Group actions on one-manifolds II: extensions of Hölder's Theorem. To appear in Trans. Amer. Math. Soc.) seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. Plante and Thurston proved that every nilpotent subgroup of Diff2(S 1) is abelian. One of our main results is a sharp converse: Diff 1 (S1) contains every finitely generated, torsion-free nilpotent group.

Original languageEnglish (US)
Pages (from-to)1467-1484
Number of pages18
JournalErgodic Theory and Dynamical Systems
Issue number5
StatePublished - Oct 2003

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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