Existence of Anosov diffeomorphisms on infra-nilmanifolds modeled on free nilpotent Lie groups
DOI:
https://doi.org/10.12775/TMNA.2015.042Keywords
Anosov diffeomorphism, infra-nilmanifold, freenilpotent Lie groupAbstract
An infra-nilmanifold is a manifold which is constructed as a~quotient space $\Gamma\setminus G$ of a simply connected nilpotent Lie group $G$, where $\Gamma$ is a discrete group acting properly discontinuously and cocompactly on~$G$ via so called affine maps. The manifold $\Gamma\setminus G$ is said to be modeled on the Lie group~$G$. This class of manifolds is conjectured to be the only class of closed manifolds allowing an Anosov diffeomorphism. However, it is far from obvious which of these infra-nilmanifolds actually do admit an Anosov diffeomorphism. In this paper we completely solve this question for infra-nilmanifolds modeled on a free $c$-step nilpotent Lie group.Downloads
Published
2015-09-01
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1.
DEKIMPE, Karel and DERÉ, Jonas. Existence of Anosov diffeomorphisms on infra-nilmanifolds modeled on free nilpotent Lie groups. Topological Methods in Nonlinear Analysis. Online. 1 September 2015. Vol. 46, no. 1, pp. 165 - 189. [Accessed 23 April 2024]. DOI 10.12775/TMNA.2015.042.
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