New proofs of theorems of Kathryn Mann

2013/08/25 by Shigenori Matsumoto, Matsumoto, Shigenori
Mathematics · #57S05 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GT #msc:57S05

paper · pdf · doi:10.48550/arxiv.1308.5381

4 pages

openalex publication_date 2013/08/25 · arxiv created 2013/09/06 · arxiv updated 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a shorter proof of the following theorem of Kathryn Mann \citeM: the identity component of the group of the compactly supported C^r diffeomorphisms of \Rⁿ cannot admit a nontrivial C^p-action on S¹, provided n≥2, r≠ n+1 and p≥2. We also give a new proof of another theorem of Mann: any nontrivial endomorphism of the group of the orientation preserving C^r diffeomorphisms of the circle is the conjugation by a C^r diffeomorphism, if r≥3.

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