
Introduction to the Geometry of Foliations, Part B
Foliations of Codimension One
Vieweg+Teubner Verlag
2nd Edition
Published on 1. January 1987
Book
Paperback/Softback
X, 298 pages
978-3-528-18568-8 (ISBN)
Description
"The book ...is a storehouse of useful information for the mathematicians interested in foliation theory." (John Cantwell, Mathematical Reviews 1992)
More details
Series
Edition
Second Edition 1987
Language
English
Place of publication
Wiesbaden
Germany
Publishing group
Vieweg & Teubner
Target group
Professional and scholarly
Professional/practitioner
Illustrations
X, 298 p.
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 17 mm
Weight
590 gr
ISBN-13
978-3-528-18568-8 (9783528185688)
DOI
10.1007/978-3-322-90161-3
Schweitzer Classification
Content
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.