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Groups of homeomorphisms of one-manifolds, I: actions of nonlinear groups

Benson Farb·John Franks
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Abstract

This self-contained paper is part of a series \cite{FF2,FF3} on actions by diffeomorphisms of infinite groups on compact manifolds. The two main results presented here are: 1) Any homomorphism of (almost any) mapping class group or automorphism group of a free group into $\Diff_+^r(S^1), r\geq 2$ is trivial. For r=0 Nielsen showed that in many cases nontrivial (even faithful) representations exist. Somewhat weaker results are proven for finite index subgroups. 2) We construct a finitely-presented group of real-analytic diffeomorphisms of $\R$ which is not residually finite.

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Benson Farb, John Franks. 2001-07-12. Groups of homeomorphisms of one-manifolds, I: actions of nonlinear groups. https://arxiv.org/abs/math/0107085

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