Ya'acov Peterzil, Sergei Starchenko

Research output: Contribution to journalArticlepeer-review


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 W G !G=Γ the quotient map. For a semialgebraic 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. We also prove an equidistribution result in the case of curves.

Original languageEnglish
Pages (from-to)3935-3976
Number of pages42
JournalDuke Mathematical Journal
Issue number18
StatePublished - 1 Dec 2022

Bibliographical note

Funding Information:
Peterzil’s work was partially supported by Israel Science Foundation grant 290/19. Starchenko’s work was partially supported by National Science Foundation grant DMS-1500671.

Publisher Copyright:
© 2022 Duke University Press. All rights reserved.

ASJC Scopus subject areas

  • Mathematics (all)


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