Actions of groups of diffeomorphisms on one-manifolds

2013/09/03 by Shigenori Matsumoto, Matsumoto, Shigenori
Mathematics · #57S05 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1309.0618

openalex publication_date 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Denote by \DC(M)₀ the identity component of the group of compactly supported C^∞ diffeomorphisms of a connected C^∞ manifold M, and by \HR the group of the homeomorphisms of \R. We show that if M is a closed manifold which fibers over S^m (m≥ 2), then any homomorphism from \DC(M)₀ to \HR is trivial.

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