Colloquium Mathematicum, Vol.XLVII, 1982, Fasc.2, 267-282.
publications
Lie groupoids have appeared in many problems of differential geometry of higher order, e.g., in the thories of connections of higher order, G-structures of higher order, pseudogroups, and in some theory of differential equations (Lie equations). Originally (C.Ehresmann, 1951), Lie groupoids were associated with principal fibre bundles. Ngo Van Que formulated in 1967 a precise abstract definition of these objects. The development of the general theory of Lie groupoids can be found in the papers of J.Pradines, A.Kumpera, R.Brown, A.Fujimoto, P.Libermann, E.Pourreza, A.K.Seda. A.Kumpera defined in 1971 an exponential mapping for Lie groupoids. This paper is devoted to a closer examination of this notion.