Introduction to the geometry of foliations

InhaltsverzeichnisIV — Basic Constructions and Examples.1. General setting in co dimension one.2. Topological dynamics.3. foliated bundles ; example.4. Gluing foliations together.5. Turbulization.6. Co dimension-one foliations on spkeres.V — Structure of Codimension-one Foliations.1. Trans verse orientability.2. Holonomy of compact leaver.3. Saturated open sets of compact manifolds.4. Centre of a compact foliated manifold; global stability.Charter VI — Exceptional Minimal Sets of Compact Foliated Manifolds; a Theorem of Sacksteder.1. Resilient leaves.2. The. theorem of Denjoy-Sacksteder.3. Sacksteder’s theorem.4. The theorem of Schwartz.Charter VII — One Sided Holonomy; Vanishing Cycles and Closed Transversals.1. Preliminaries on one-sided holonomy and vanishing cycles.2. Transverse follatlons of D2 × IR.3. Existence of one-sided holonomy and vanishing cycles.VIII — Foliations Without Holonomy.1. Closed 1-forms without singularities.2. Foliations without holonomy versus equivariant fibrations.3. Holonomy representation and cohomology direction.IX — Growth.1. Growth of groups, homogeneous spaces and riemannian manifolds.2. Growth of leaves in foliations on compact manifolds.X — Holonomy Invariant Measures.1. Invariant measures for subgroups of Horneo (IR) or Homeo (S1 ).2. Foliations witk holonomy invariant measure.Literature..Glossary of notations.