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Pradines, Jean

How to define the differentiable graph of a singular foliation. (English) Zbl 0576.57023

Cah. Topol. Géom. Différ. Catégoriques 26, 339-380 (1985).
This paper is devoted to the generalization of the graph (holonomy groupoid) of a foliation [Ch. Ehresmann, Proc. fifth Canad. Math. Congr., Montreal 1961, 109-172 (1963; Zbl 0146.195); Oeuvres complètes et commentées. Catégories ordonnées, applications des ordres en topologie, Partie II, 2., Suppl. à Cah. Topologic Géom. Différ. 23, 435-778 (1982; Zbl 0529.01017), pp. 563-626; H. E. Winkelnkemper, Ann. Global Anal. Geom. 1, No.3, 51-75 (1983; Zbl 0526.53039)] to foliations with singularities in the sense of P. Stefan [Proc. Lond. Math. Soc., III. Ser. 29, 699-713 (1974; Zbl 0342.57015)].
We quote from the author’s summary: ”For a large class of singular foliations in the sense of Stefan, we construct a differentiable groupoid which generalizes the graph of a regular foliation; this attaches to every singular leaf a differentiable principal bundle which is an extension of the holonomy covering defined by Ehresmann for the locally simple topological foliations. The construction uses a diagram description of regular equivalences and their transverse isomorphisms as well as of the composition of their regular graphs. Then, this description is weakened so as to take care of the possible singularities.”
Reviewer: I.Vaisman

Cited in 2 Reviews
Cited in 13 Documents

MSC:

57R30 Foliations in differential topology; geometric theory

Keywords:

holonomy groupoid; singular foliations; differentiable groupoid; graph of a regular foliation; holonomy covering

Citations:

Zbl 0146.195; Zbl 0529.01017; Zbl 0526.53039; Zbl 0342.57015
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References:

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