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A topological groupoid \(\fancyscript{G}\) is \(K\)-pointed, if it is equipped with a homomorphism from a topological group \(K\) to \(\fancyscript{G}\). We describe the homotopy groups of such \(K\)-pointed topological groupoids and relate these groups to the ordinary homotopy groups in terms of a long exact sequence. As an application, we give an obstruction to presentability of proper regular Lie groupoids.

Homotopy sequence of a topological groupoid with a basegroup and an obstruction to presentability of proper regular Lie groupoids