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arXiv · 1201.3595

The space of Anosov diffeomorphisms

F. Thomas Farrell·Andrey Gogolev
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Abstract

We consider the space $\X$ of Anosov diffeomorphisms homotopic to a fixed automorphism $L$ of an infranilmanifold $M$. We show that if $M$ is the 2-torus $\mathbb T^2$ then $\X$ is homotopy equivalent to $\mathbb T^2$. In contrast, if dimension of $M$ is large enough, we show that $\X$ is rich in homotopy and has infinitely many connected components.

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BibTeXRIS

F. Thomas Farrell, Andrey Gogolev. 2012-01-17. The space of Anosov diffeomorphisms. https://doi.org/10.1112/jlms%2Fjdt073

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