First Neighbourhood of the Diagonal, and Geometric Distributions

Abstract

For any manifold, we describe the notion of geometric distribution on it, in terms of its first neighbourhood of the diagonal. In these “combinatorial” terms, we state the Frobenius Integrability Theorem, and use it to give a combinatorial proof of the Ambrose–Singer Theorem on connections in principal bundles. The consideration of the k’th neighbourhood of… (More)

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