The diffential geometry of composition sequences of differentiable manifolds

Details The diffential geometry of composition sequences of differentiable manifolds The diffential geometry of composition sequences of differentiable manifolds

2002-10-07

arxiv.org/abs/math/0210102v2

Mathematics

Differential Geometry

13 pages, 10 references, we define the notion of holonomy in this version

Scientific paper

Let F_0=B,...,F_n be a sequence of differentiable manifolds, G_i a Lie subgroup of diffeomorphisms of F_i, and H_i a subgroup of G_i central in G_i. We suppose also given a locally trivial bundle p_{K_i} over F_{i-1} which typical fiber is K_i the quotient of G_i by H_i. The aim of this paper is to study the differential geometry of the following problem: classify sequences M_n\to...M_1, where each map from M_i to M_{i-1} is a locally trivial fibration which typical fiber is F_i and which transition functions image are elements of G_i. 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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