Geometry of compact lifting spaces

Gregory R. Conner; Wolfgang Herfort; Petar Pavešić

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arXiv · 1901.02108

Geometry of compact lifting spaces

Gregory R. Conner·Wolfgang Herfort·Petar Pavešić

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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.

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BibTeX RIS

Gregory R. Conner, Wolfgang Herfort, Petar Pavešić. 2019-01-07. Geometry of compact lifting spaces. https://arxiv.org/abs/1901.02108

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