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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.

The Dehn functions of O u t ( F n ) and A u t ( F n )

Martin R. Bridson, Karen Vogtmann (2012)

Annales de l’institut Fourier

For n at least 3, the Dehn functions of O u t ( F n ) and A u t ( F n ) are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case n = 3 was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for n bigger than 3 to the case n = 3 . In this note we give a shorter, more direct proof of this last reduction.

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