Transversal local rigidity of discrete Abelian actions on Heisenberg nilmanifolds

Abstract

In this paper we prove a perturbative result for a class of $\mathbb Z^2$ actions on Heisenberg nilmanifolds, which have Diophantine properties. Along the way we prove cohomological rigidity and obtain a tame splitting for the cohomology with coefficients in smooth vector fields for such actions.