Groupoids of Local Isometries

  • Martin R. Bridson
  • André Haefliger
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 319)


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.


Fundamental Group Galois Group Homotopy Class Differentiable Manifold Riemannian Submersion 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Martin R. Bridson
    • 1
  • André Haefliger
    • 2
  1. 1.Mathematical InstituteUniversity of OxfodOxfordGreat Britain
  2. 2.Section de MathématiquesUniversité de GenèveGenève 24Switzerland

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