Serre fibrations in the Morita category of topological groupoids

In this paper, we generalize the notion of Serre fibration to the Morita category of topological groupoids and derive the associated long exact sequence of homotopy groups. We use this results for calculation of homotopy groups of various groupoids, such as the foliation groupoid of a Riemannian fol...

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Bibliographic Details
Published in:Topology and its applications 2013-01, Vol.160 (1), p.9-23
Main Author: Jelenc, Blaž
Format: Article
Language:English
Subjects:
Foliations
Homotopy groups
Morita category
Serre fibrations
Topological groupoids
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Summary:In this paper, we generalize the notion of Serre fibration to the Morita category of topological groupoids and derive the associated long exact sequence of homotopy groups. We use this results for calculation of homotopy groups of various groupoids, such as the foliation groupoid of a Riemannian foliation.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2012.09.013