\(n\)-transitivity of bisection groups of a Lie groupoid (Q2404093)

This paper studies the notion of \(n\)-transitivity for the group of bisections of a Lie groupoid. Let us recall that Lie groupoids generalize Lie groups and that important features of Lie theory can be carried over to Lie groupoids. In this work, the author generalizes the notion of \(n\)-transtivity for Lie groupoids. It was proved by \textit{D. Zhong} et al. [Acta Math. Sin., Engl. Ser. 25, No. 6, 1001--1014 (2009; Zbl 1221.58015)] that under some conditions a bisection group of a Lie groupoid is \(n\)-transitive. Here, the author generalizes this result in several aspects. For instance, he shows that the group of all bisections of any Lie groupoid and the group of all Lagrangian bisections of a symplectic manifold are \(n\)-transtive.