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1 December 2021 O-minimal flows on nilmanifolds
Ya’acov Peterzil, Sergei Starchenko
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Duke Math. J. 170(18): 3935-3976 (1 December 2021). DOI: 10.1215/00127094-2021-0008

Abstract

Let G be a connected, simply connected nilpotent Lie group, identified with a real algebraic subgroup of UT(n,R), and let Γ be a lattice in G, with π:GGΓ the quotient map. For a semialgebraic XG, and more generally a definable set in an o-minimal structure on the real field, we consider the topological closure of π(X) in the compact nilmanifold GΓ.

Our theorem describes cl(π(X)) in terms of finitely many families of cosets of real algebraic subgroups of G. The underlying families are extracted from X, independently of Γ. We also prove an equidistribution result in the case of curves.

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Ya’acov Peterzil. Sergei Starchenko. "O-minimal flows on nilmanifolds." Duke Math. J. 170 (18) 3935 - 3976, 1 December 2021. https://doi.org/10.1215/00127094-2021-0008

Information

Received: 26 January 2019; Revised: 19 March 2020; Published: 1 December 2021
First available in Project Euclid: 22 November 2021

Digital Object Identifier: 10.1215/00127094-2021-0008

Subjects:
Primary: 03C64
Secondary: 37A17

Keywords: nilmanifolds , o-minimal , Ratner’s theorem , unipotent groups

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 18 • 1 December 2021
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