On the Existence of Cross Sections in Locally Flat Bundles
نویسنده
چکیده
1. A principal bundle 33(X, G) with base space X and group G is called "locally flat" if the structural group G can be reduced to a totally disconnected subgroup GiCG, or in other words: if there exists a totally disconnected subgroup GiQG, a principal bundle 33i(X, Gi) and an injection j: Soi—>33 [l ]. For instance, if a differentiable bundle 33 admits an infinitesimal connection whose curvature form is identically zero, then S3 is locally flat [l, Reduction theorem, p. 37]. We are mainly interested in locally flat bundles with arcwise connected structural group G. The aim of this note is to give necessary and sufficient conditions for locally flat bundles to have a cross section.
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