2014/03/30 by Kiran Parkhe, Parkhe, Kiran
Mathematics · #20F18 #37E05 #37E10 #57S25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #math.GR #msc:20F18 #msc:37E05 #msc:37E10 #msc:57S25
paper · pdf · doi:10.48550/arxiv.1403.7781
16 pages
openalex publication_date 2014/03/30 · arxiv created 2014/09/26 · arxiv updated 2014/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a connected 1-manifold, i.e., M = \R ≅ (0, 1), [0, 1), [0, 1], or S1, and let \Homeo+(M) (resp. \Diff+1(M)) be the group of orientation-preserving homeomorphisms (resp. C1 diffeomorphisms) of M. It is a classical result that if N is a finitely-generated, torsion-free nilpotent group, then there exist 1-1 homomorphisms ϕ\colon N → \Homeo+(M). Farb and Franks show that, in fact, there exists a 1-1 homomorphism N → \Diff+1(M). In this paper we obtain a stronger result: every action ϕ\colon N → \Homeo+(M) is topologically conjugate to an action ϕ\colon N → \Diff+1(M).