Submission date: 14 September 2018

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 : G → G/Γ the quotient map. For a semi-algebraic X ⊆ G, 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 G/Γ.
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.

Mathematics Subject Classification: 03C64, 37A

Keywords and phrases:

Full text arXiv 1809.05460: pdf, ps.