Abstract:
Suppose given a nilpotent connected simply connected Lie group
$G$,
a
connected Lie subgroup
$H$
of
$G$,
and a discontinuous group
$\Gamma$
for the homogeneous space
$\mathscr{M}=G/H$.
In this work we study the topological stability of the parameter
space
$\mathscr{R}(\Gamma,G,H)$
in the case where
$G$
is three-step.
We prove
a stability theorem for certain particular pairs
$(\Gamma,H)$.
We also introduce
the notion of strong stability on layers making use of an explicit layering of
$\mathrm{Hom}(\Gamma,G)$
and study the case of Heisenberg groups.
Keywords:parameter space, stability, Heisenberg groups, strong stability on layers.
