The space of Anosov diffeomorphisms

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.

Version 2: referee suggestions result in a better exposition

References in corpus (1)

• Operations on A-theoretic nil-terms