Introduction to the Geometry of Foliations, Part B

Foliations of Codimension One
2. Auflage 1987
ISBN: 978-3-528-18568-8
Verlag: Vieweg+Teubner Verlag

Buch, Englisch, Band 3, 298 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 590 g

Reihe: Aspects of Mathematics

"The book.is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Hector, Gilbert

Hirsch, Ulrich

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie

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.