Open Access
April 2015 Deforming discontinuous subgroups of reduced Heisenberg groups
Ali Baklouti, Sonia Ghaouar, Fatma Khlif
Kyoto J. Math. 55(1): 219-242 (April 2015). DOI: 10.1215/21562261-2848169


Let G=H2n+1r be the (2n+1)-dimensional reduced Heisenberg group, and let H be an arbitrary connected Lie subgroup of G. Given any discontinuous subgroup ΓG for G/H, we show that resulting deformation space T(Γ,G,H) of the natural action of Γ on G/H is endowed with a smooth manifold structure and is a disjoint union of open smooth manifolds. Unlike the setting of simply connected Heisenberg groups, we show that the stability property holds and that any discrete subgroup of G is stable, following the notion of stability. On the other hand, a local (and hence global) rigidity theorem is obtained. That is, the related parameter space R(Γ,G,H) admits a rigid point if and only if Γ is finite.


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Ali Baklouti. Sonia Ghaouar. Fatma Khlif. "Deforming discontinuous subgroups of reduced Heisenberg groups." Kyoto J. Math. 55 (1) 219 - 242, April 2015.


Published: April 2015
First available in Project Euclid: 13 March 2015

zbMATH: 1317.22006
MathSciNet: MR3323533
Digital Object Identifier: 10.1215/21562261-2848169

Primary: 22E27
Secondary: 32G05

Keywords: deformation space , free action , proper action , Reduced Heisenberg group , rigidity

Rights: Copyright © 2015 Kyoto University

Vol.55 • No. 1 • April 2015
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