Groupoids of Local Isometries
The purpose of this chapter is to prove a general result concerning the developability of groupoids of local isometries. We shall show that if such a groupoid G is Hausdorff and complete (in a suitable sense, 2.10), and if the metric on the space of units of G is locally convex, then G is equivalent to the groupoid associated to the proper action of a group of isometries on a complete geodesic space whose metric is (globally) convex in the sense of (II.1.3). This result unifies and extends several earlier developability theorems, as we shall now explain.
KeywordsFundamental Group Galois Group Homotopy Class Differentiable Manifold Riemannian Submersion
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