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Monodromy and faithful representability of Lie groupoids. (English) Zbl 1388.22002

The author constructs an associated monodromy group \(\mathrm{Mon}(\mathcal G,\rho)\) for any topological groupoid \(\mathcal G\) and any homomorphism \(\rho\) from a locally compact Hausdorff topological group \(K\) to \(\mathcal G\). He proves that Morita equivalent topological groupoids have the same monodromy groups. He also shows how the monodromy groups can be used to test if a Lie groupoid lacks faithful representations.

MSC:

22A22 Topological groupoids (including differentiable and Lie groupoids)
58H05 Pseudogroups and differentiable groupoids
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References:

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