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Rational sub-nilmanifolds of a compact nilmanifold

Published online by Cambridge University Press:  18 April 2006

A. LEIBMAN
A. LEIBMAN
Affiliation:
Department of Mathematics, The Ohio State University, OH 43221, USA (e-mail: leibman@math.ohio-state.edu)
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Abstract

We introduce the notions of a rational point, a rational sub-nilmanifold and a rational homomorphism of compact nilmanifolds and describe elementary properties thereof. We also show that the closure of the orbit of a point of a nilmanifold $X$ under a polynomial action of the group $\mathbb{Z}^{d}$ by translations is, up to a shift, a union of rational sub-nilmanifolds of $X$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 3 , June 2006 , pp. 787 - 798
Copyright
2006 Cambridge University Press

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