Introduction to the Geometry of Foliations, Part B: Foliations of Codimension One Aspects of Mathematics

Gilbert Hector & Ulrich Hirsch

ISBN 10: 3528085681 / ISBN 13: 9783528085681

Editore: Friedrick Vieweg & Son, 1984

298 pp., paperback, fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Codice articolo ZB1303204

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Contenuti: 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 × 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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Titolo: Introduction to the Geometry of Foliations, ...
Casa editrice: Friedrick Vieweg & Son
Data di pubblicazione: 1984
Legatura: Brossura
Condizione: Fine