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The C 1 generic diffeomorphism has trivial centralizer

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Abstract

Answering a question of Smale, we prove that the space of C 1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.

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Authors and Affiliations

  1. CNRS–Institut de Mathématiques de Bourgogne, UMR 5584, BP 47 870, 21078, Dijon Cedex, France

    Christian Bonatti

  2. CNRS–LAGA, UMR 7539, Université Paris 13, 99 Avenue J.-B. Clément, 93430, Villetaneuse, France

    Sylvain Crovisier

  3. Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL, 60208-2730, USA

    Amie Wilkinson

Authors
  1. Christian Bonatti
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  2. Sylvain Crovisier
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  3. Amie Wilkinson
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Correspondence to Sylvain Crovisier.

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Bonatti, C., Crovisier, S. & Wilkinson, A. The C 1 generic diffeomorphism has trivial centralizer. Publ.math.IHES 109, 185–244 (2009). https://doi.org/10.1007/s10240-009-0021-z

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  • DOI: https://doi.org/10.1007/s10240-009-0021-z

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