%0 Journal Article
%T Nilpotent extensions of minimal homeomorphisms
%A Gernot Greschonig
%A Ulrich Haboeck
%J Mathematics
%D 2005
%I arXiv
%X In this paper we study topological cocycles for minimal homeomorphisms on a compact metric space. We introduce a notion of an essential range for topological cocycles with values in a locally compact group, and we show that this notion coincides with the well known topological essential range if the group is abelian. We define then a regularity condition for cocycles and prove several results on the essential ranges and the orbit closures of the skew product of regular cocycles. Furthermore we show that recurrent cocycles for a minimal rotation on a locally connected compact group are always regular, supposed that their ranges are in a nilpotent group, and then their essential ranges are almost connected.
%U http://arxiv.org/abs/math/0502431v1