The Simplicity of Diffeomorphism Groups
It was known since 1961 (Anderson ) 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.
KeywordsNormal Subgroup Simple Group Open Cover Smooth Manifold Implicit Function Theorem
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