A new method for constructing Anosov Lie algebras
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.
Cite
@article{arxiv.1312.2872,
title = {A new method for constructing Anosov Lie algebras},
author = {Jonas Deré},
journal= {arXiv preprint arXiv:1312.2872},
year = {2015}
}
Comments
18 pages, some small revisions according to referee report, to appear in Transactions of the AMS