TY - JOUR
T1 - O-MINIMAL FLOWS on NILMANIFOLDS
AU - Peterzil, Ya'acov
AU - Starchenko, Sergei
N1 - 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.
PY - 2022/12/1
Y1 - 2022/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85122127825&partnerID=8YFLogxK
U2 - https://doi.org/10.1215/00127094-2021-0008
DO - https://doi.org/10.1215/00127094-2021-0008
M3 - Article
SN - 0012-7094
VL - 170
SP - 3935
EP - 3976
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 18
ER -