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A new method for constructing Anosov Lie algebras


Author: Jonas Deré
Journal: Trans. Amer. Math. Soc. 368 (2016), 1497-1516
MSC (2010): Primary 37D20; Secondary 22E25, 20F34
DOI: https://doi.org/10.1090/tran6655
Published electronically: June 15, 2015
MathSciNet review: 3430371
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Abstract: It is conjectured that every closed 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 new examples which were overlooked in 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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Additional Information

Jonas Deré
Affiliation: KU Leuven Kulak, E. Sabbelaan 53, 8500 Kortrijk, Belgium
Email: jonas.dere@kuleuven-kulak.be

DOI: https://doi.org/10.1090/tran6655
Received by editor(s): December 10, 2013
Received by editor(s) in revised form: June 26, 2014, and November 18, 2014
Published electronically: June 15, 2015
Additional Notes: The author was supported by a Ph.D. fellowship of the Research Foundation – Flanders (FWO). Research supported by the research Fund of the KU Leuven
Article copyright: © Copyright 2015 American Mathematical Society