Group actions on one-manifolds, II: Extensions of Hölder's theorem

Benson Farb*, John Franks

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

This self-contained paper is part of a series seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. In this paper we consider groups which act on R with restrictions on the fixed point set of each element. One result is a topological characterization of affine groups in Diff22 (R) as those groups whose elements have at most one fixed point.

Original languageEnglish (US)
Pages (from-to)4385-4396
Number of pages12
JournalTransactions of the American Mathematical Society
Volume355
Issue number11
DOIs
StatePublished - Nov 2003

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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