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The C 1 generic diffeomorphism has trivial centralizer

Christian Bonatti, Sylvain Crovisier, Amie Wilkinson (2009)

Publications Mathématiques de l'IHÉS

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.

Topological conjugacy of locally free 𝐑 n - 1 actions on n -manifolds

David C. Tischler, Rosamond W. Tischler (1974)

Annales de l'institut Fourier

For actions as in the title we associate a collection of rotation numbers. If one of them is sufficiently irrational then the action is conjugate (as an action) to either a linear action on a torus or to an action on a principal T k bundle over T 2 with T k × R 1 orbits.

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