Holonomy and the Stability Theorems

César Camacho and Alcides Lins Neto

Chapter IV in Geometric Theory of Foliations, 1985, pp 61-85 from Springer

Abstract: Abstract In this chapter F denotes a foliation of codimension n and class C r , r ≥ 1, of a manifold M m . Our objective is to study the behavior of the leaves near a fixed compact leaf F. By the transverse uniformity of F it is sufficient to study the first returns of leaves to a small transverse section Σ of dimension n passing through a point p ∈ F. For each closed path γ in F passing through p, these returns can be expressed by a local C r diffeomorphism of Σ, f γ, with f γ (p) = p and where for x ∈ Σ sufficiently near p, f γ(x) is the first return “over γ” of the leaf of F which passes through x.

Keywords: Vector Field; Neighborhood Versus; Geometric Theory; Integral Curve; Stability Theorem (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-5292-4_5

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DOI: 10.1007/978-1-4612-5292-4_5

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