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arXiv · 1312.2872

A new method for constructing Anosov Lie algebras

Jonas Deré
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Abstract

It is conjectured that every manifold admitting an Anosov diffeomorphism is, up to homeomorphism, finitely covered by a nilmanifold. Motivated by this conjecture, an important problem is to determine which nilmanifolds admit an Anosov diffeomorphism. The main theorem of this article gives a general method for constructing Anosov diffeomorphisms on nilmanifolds. As a consequence, we give counterexamples to a corollary of the classification of low-dimensional nilmanifolds with Anosov diffeomorphisms and a correction to this statement is proven. This method also answers some open questions about the existence of Anosov diffeomorphisms which are minimal in some sense.

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Jonas Deré. 2013-12-10. A new method for constructing Anosov Lie algebras. https://arxiv.org/abs/1312.2872

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