Geometry of compact lifting spaces
Algebraic Topology
2019-01-09 v1
Abstract
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.
Cite
@article{arxiv.1901.02108,
title = {Geometry of compact lifting spaces},
author = {Gregory R. Conner and Wolfgang Herfort and Petar Pavešić},
journal= {arXiv preprint arXiv:1901.02108},
year = {2019}
}