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

Published electronically:
July 8, 2003

MathSciNet review:
1986507

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Abstract | References | Similar Articles | Additional Information

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 with restrictions on the fixed point set of each element. One result is a topological characterization of affine groups in 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