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Homotopy sequence of a topological groupoid with a basegroup and an obstruction to presentability of proper regular Lie groupoids. (English) Zbl 1329.22005

Topological groupoids are geometric objects representing singular quotient spaces (as foliations, equivalence relations, group actions, orbifolds, etc.).
The authors describe homotopy groups of \(K\)-pointed topological groupoids, where \(K\) is a topological group and there is a homomorphism from \(K\) to the groupoid. These homotopy groups are related to the ordinary homotopy groups through a long exact sequence. An obstruction to the presentability of proper regular Lie groupoids is given from the previous results.

MSC:

22A22 Topological groupoids (including differentiable and Lie groupoids)
55Q05 Homotopy groups, general; sets of homotopy classes
58H05 Pseudogroups and differentiable groupoids
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