Introduction to the Geometry of Foliations, Part B

Inhaltsverzeichnis

• IV — 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.