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

2001/07/11 by Benson Farb, John Franks, Farb, Benson +1
Mathematics · #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0107085

openalex publication_date 2001/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This self-contained paper is part of a series \citeFF2,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(S¹), r≥ 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.

Related

• Actions of groups of homeomorphisms on one-manifolds
• Actions of groups of diffeomorphisms on one-manifolds
• Reconstructing maps out of groups
• Structure theorems for actions of homeomorphism groups
• There are no exotic actions of diffeomorphism groups on 1-manifolds