Geometry of compact lifting spaces. (arXiv:1901.02108v1 [math.AT])
We study a natural generalization of inverse systems of finite regular
covering spaces. A limit of such a system is a fibration whose fibres are
profinite topological groups. However, as shown in a previous paper
(Conner-Herfort-Pavesic: Some anomalous examples of lifting spaces), there are
many fibrations whose fibres are profinite groups, which are far from being
inverse limits of coverings. We characterize profinite fibrations among a large
class of fibrations and relate the profinite topology on the fundamental group
of the base with the action of the fundamental group on the fibre, and develop
a version of the Borel construction for fibrations whose fibres are profinite
groups.查看全文