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

Farb, Benson; Franks, John

doi:10.1090/S0002-9947-03-03376-2

Group actions on one-manifolds, II: Extensions of Hölder’s Theorem
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Trans. Amer. Math. Soc. 355 (2003), 4385-4396 Request permission

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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