Abstract
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.
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© 1999 Springer-Verlag Berlin Heidelberg
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Bridson, M.R., Haefliger, A. (1999). Groupoids of Local Isometries. In: Metric Spaces of Non-Positive Curvature. Grundlehren der mathematischen Wissenschaften, vol 319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12494-9_24
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DOI: https://doi.org/10.1007/978-3-662-12494-9_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08399-0
Online ISBN: 978-3-662-12494-9
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