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


Authors: Benson Farb and John Franks
Journal: Trans. Amer. Math. Soc. 355 (2003), 4385-4396
MSC (2000): Primary 37E10
DOI: https://doi.org/10.1090/S0002-9947-03-03376-2
Published electronically: July 8, 2003
MathSciNet review: 1986507
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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 $\mathbf R$ with restrictions on the fixed point set of each element. One result is a topological characterization of affine groups in $\mathrm{Diff}^2(\mathbf R)$ as those groups whose elements have at most one fixed point.

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Additional Information

Benson Farb
Affiliation: Department of Mathematics, University of Chicago, 5734 University Ave., Chicago, Illinois 60637
Email: farb@math.uchicago.edu

John Franks
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: john@math.northwestern.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03376-2
Received by editor(s): September 6, 2001
Received by editor(s) in revised form: November 29, 2001
Published electronically: July 8, 2003
Additional Notes: The first author was supported in part by NSF grant DMS9704640
The second author was supported in part by NSF grant DMS9803346
Article copyright: © Copyright 2003 American Mathematical Society