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The diffential geometry of composition sequences of differentiable manifolds

A. Tsemo

math.DGarXiv:math/0210102

Abstract

Let F0=B,...,Fn be a sequence of differentiable manifolds, Gi a Lie subgroup of diffeomorphisms of Fi, and Hi a subgroup of Gi central in Gi. We suppose also given a locally trivial bundle pKi over Fi-1 which typical fiber is Ki the quotient of Gi by Hi. The aim of this paper is to study the differential geometry of the following problem: classify sequences Mn...M1, where each map from Mi to Mi-1 is a locally trivial fibration which typical fiber is Fi and which transition functions image are elements of Gi. We associate to this problem a tower of gerbes and define for it the notion of connective structure, curvature and holonomy using the notion of free transitive distribution (free TD)

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