Title: 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 ...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.Read More
Publication Year: 2013
Publication Date: 2013-12-10
Language: en
Type: preprint
Access and Citation
Cited By Count: 2
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot