Foliations of codimension one
著者
書誌事項
Foliations of codimension one
（Aspects of mathematics = Aspekte der Mathematik, E 3 . Introduction to the geometry of foliations ; Pt. B）
F. Vieweg & Sohn, 1983
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注記
Includes bibliographical references and index
内容説明・目次
目次
- IV - Basic Constructions and Examples.- 1. General setting in co dimension one.- 1.1. Existence of a transverse foliation.- 1.2. Holonomy pseudogroups.- 1.3. Appendix: One-dimensional foliations and local flows.- 2. Topological dynamics.- 2.1. The relation ?F and ?P.- 2.2. Leaf types
- minimal sets.- 3. Foliated bundles
- examples.- 3.1. Topological dynamics in foliated bundles.- 3.2. Fibre bundles arising as foliated bundles.- 3.3. Examples.- 4. Gluing foliations together.- 4.1. Gluing together foliations tangent to the boundary.- 4.2. Gluing together foliations transverse to the boundary.- 5. Turbulization.- 5.1. Closed transversals.- 5.2. Turbulization along a closed transversal or along a boundary component.- 6. Codimension-one foliations on spheres.- 6.1. Manifolds as open books.- 6.2. Foliations on odd-dimensional spheres.- V - Structure of Codimension-One Foliations.- 1. Transverse orientability.- 1.1. Transverse orientability
- one- and two-sided leaves.- 1.2. Forms and linear holonomy.- 2. Holonomy of compact leaves.- 2.1. Local diffeomorphisms of the real line.- 2.2. Germ near a compact leaf
- local stability.- 3. Saturated open sets of compact manifolds.- 3.1. Semi-proper leaves
- completion of saturated open sets.- 3.2. The structure of saturated open sets.- 4. Centre of a compact foliated manifold
- global stability.- 4.1. Structure of the centre.- 4.2. The global stability theorems of Reeb and Thurston.- 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.- VII - One Sided Holonomy
- Vanishing Cycles and Closed Transversals.- 1. Preliminaries on one-sided holonomy and vanishing cycles.- 2. Transverse foliation* of D2 x IR.- 2.1. Foliations with singularities on the disk.- 2.2. One-sided holonomy in transverse foliations.- 3. Existence of one-sided holonomy and vanishing cycles.- VIII - Foliations without Holonomy.- 1. Closed 1-forms without singularities.- 1.1. Closed 1-forms and foliations obtained by an equivariant fibration.- 1.2. The theorem of Tischler.- 2. Foliations without holonomy versus equivariant fibrations.- 2.1. Trivialization and global unwrapping.- 2.2. Trivializing foliations without kolonomy.- 3. Holonomy representation and cohomology direction.- 3.1. Holder's theorem
- fixed point free subgroups of Homeo (IR).- 3.2. Foliations witkout kolonomy and closed 1-forms.- IX - Growth.- 1. Growth of groups, homogeneous spaces and riemannian manifolds.- 1.1. Growth type, of functions.- 1.2. Growth of finitely generated groups and komogeneous spaces.- 1.3. Growth of riemannian manifolds
- application to covering spaces.- 2. Growth of leave in foliatoons on compact manifolds.- 2.1. Growth of leaves in topological foliations.- 2.2. Growth of leaves in differentiable foliations.- X - Holonomy Invariant Measures.- 1. Invariant measures for subgroups of Homeo (?) or Homeo(S1).- 1.1. Abelianization of subgroups of Homeo+(IR) admitting an invariant measure.- 1.2. Diffuse measures versus Lebesgue measure
- invariant measures on S1.- 2. Foliations with holonomy invariant measure.- 2.1. Fundamentals on holonomy invariant measures.- 2.2. Averaging sequences and kolonomy invariant measunres.- 2.3. Holonomy invariant measures for foliations of codimension one.
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