Groups of homeomorphisms of onemanifolds, I: actions of nonlinear groups
Abstract
This selfcontained 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 finitelypresented group of realanalytic diffeomorphisms of $\R$ which is not residually finite.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2001
 arXiv:
 arXiv:math/0107085
 Bibcode:
 2001math......7085F
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 28 pages