The space of Anosov diffeomorphisms

Details The space of Anosov diffeomorphisms The space of Anosov diffeomorphisms

2012-01-17

arxiv.org/abs/1201.3595v1

Mathematics

Dynamical Systems

Scientific paper

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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