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The Simplicity of Diffeomorphism Groups

  • Augustin Banyaga
Part of the Mathematics and Its Applications book series (MAIA, volume 400)

Abstract

It was known since 1961 (Anderson [2]) that the group of stable homeomorphisms of a manifold is a simple group. Later on, the work of Chernavski, Kirby and Edwards showed that the group of stable homeomorphisms is the same as the group of homeomorphisms isotopic to the identity. This led Smale to conjecture that the group Diff r (M)0 of C r diffeomorphismss of a smooth manifold M, with compact supports, isotopic to the identity, with compactly supported isotopies, should be simple.

Keywords

Normal Subgroup Simple Group Open Cover Smooth Manifold Implicit Function Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Augustin Banyaga
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUSA

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