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Wednesday, July 8, 2020 | History

3 edition of Characteristic classes of foliations found in the catalog.

Characteristic classes of foliations

H. V. Pittie

Characteristic classes of foliations

by H. V. Pittie

  • 180 Want to read
  • 34 Currently reading

Published by Pitman Pub. in London, San Francisco .
Written in English

    Subjects:
  • Foliations (Mathematics),
  • Characteristic classes.

  • Edition Notes

    Bibliography: p. 106-107.

    StatementH. V. Pittie.
    SeriesResearch notes in mathematics ;, 10
    Classifications
    LC ClassificationsQA613.62 .P57
    The Physical Object
    Pagination107 p. ;
    Number of Pages107
    ID Numbers
    Open LibraryOL4893490M
    ISBN 100273003119
    LC Control Number76026499

    ations. This fact reflects in the secondary characteristic classes. For example, all the secondary classes of smooth foliations are zero on Riemannian foliations, but some of the secondary classes of holomorphic foliations may be non-zero on Kahler foliations. A new ingredient of our context is the Kahler form. D Foliations from the dynamical view point 6 E Stability problems 7 F Classifying spaces and characteristic classes 8 G Riemannian geometry of foliations 15 H Other topics 15 The following collection of questions in the theory of foliations are a sampling of the many open problems in the eld. They where collected mainly from.

    Two foliations and on are called concordant if there is a foliation on the "cylinder" (having the same codimension) whose leaves are transversal to the "floor" and "roof" of the cylinder and "cut out" on them the foliations and, respectively. Concordance of Haefliger structures is defined in a similar way. 3 Foliations One can think of a foliation as an equivalence relation on an m-manifold M in which the equivalence classes are connected, immersed submanifolds of a common dimension k. Locally, the equivalence classes should be analogous to the “leaves” of Rk which make up Rm. We shall be more precise before turning to some examples. Size: KB.

    In mathematics, a characteristic class is a way of associating to each principal bundle on a topological space X a cohomology class of X. The cohomology class measures the extent to which the bundle is twisted particularly, whether it possesses&#;. Characteristic classes of foliations 3 the kernels of the differentials of the submersions p t form the integrable p-dimensional subbundle of the tangent bundle. 3. Generalized foliations (foliations with singularities). Each definition given in § can be modified in a natural way to give a definition of a foliation with by:


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Characteristic classes of foliations by H. V. Pittie Download PDF EPUB FB2

The author moves on to the characteristic classes of foliations in chapter 3. This is a topic very important to those who study dynamical systems, and the author gives a pretty good overview of how characteristic classes can measure the global properties of by: Characteristic classes of foliations. London ; San Francisco: Pitman Pub., © Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: H V Pittie.

Find more information about: ISBN: # Characteristic. Lectures on characteristic classes and foliations [Raoul Bott] on *FREE* shipping on qualifying : Raoul Bott. Characteristic classes are elements of cohomology groups; one can obtain integers from characteristic classes, called characteristic important examples of characteristic numbers are Stiefel–Whitney numbers, Chern numbers, Pontryagin numbers, and the Euler characteristic.

Given an oriented manifold M of dimension n with fundamental class [] ∈ (), and a G-bundle with. The characteristic fibrations are linked to the codimension–1 regular Characteristic classes of foliations book on M. In particular, we prove that the characteristic classes of such foliations coincide with the Stiefel Author: Igor Nikolaev.

They include characteristic classes of flat bundles, characteristic classes of foliations, and characteristic classes of surface bundles. The book is intended for graduate students and research mathematicians working in various areas of geometry and topology.

I.N. Bernshtein, B.I. Rozenfel’d, Homogeneous spaces of infinite dimensional Lie algebras and characteristic classes of foliations, Uspekhi Mat. Nauk 28 (4()) () – [3] D.B. Fuks, Characteristic classes of foliations, Russian by: 3.

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds.

Cite this chapter as: Bott R. () Lectures on characteristic classes and foliations. In: Lectures on Algebraic and Differential by: [BH] R. Bott and A. Haefliger, On characteristic classes of Г-foliations, Bull.

Amer. Math. Soc. 78 (), Zentralblatt MATH: Mathematical Reviews (MathSciNet): MR [BHI] R. Bott and J. Heitsch, A remark on the integral cohomology of BT q, Topology 11 (), Characteristic classes of Lagrangian foliations Article (PDF Available) in Functional Analysis and Its Applications 23(2) April with 24 Reads How we measure 'reads'Author: Serge Tabachnikov.

Foliations.- Foliated bundles.- Characteristic classes of flat bundles.- Characteristic classes of foliated bundles.- Cohomology of g-DG-algebras.- Non-trivial characteristic classes for flat bundles.- Examples of generalized characteristic classes for foliated bundles.- Semi-simplicial weil algebras.

Baker, D.: On a class of foliations and the evaluation of their characteristic classes. Bull. Amer. Math. Soc, – () Google ScholarCited by: 7. For this volume, the authors have selected three special topics: analysis on foliated spaces, characteristic classes of foliations, and foliated manifolds.

Each of these is an example of deep interaction between foliation theory and some other highly-developed area of mathematics. Characteristic classes for Riemannian foliations Steven Hurder Department of Mathematics (m/c ) University of Illinois at Chicago Chicago, ILUSA E-mail: [email protected] The purpose of this paper is to both survey and o er some new results on the non-triviality of the characteristic classes of Riemannian foliations.

We give. For this volume, the authors have selected three special topics: analysis on foliated spaces, characteristic classes of foliations, and foliated manifolds. Each of these is an example of deep interaction between foliation theory and some other highly-developed area of mathematics.

In all cases, the authors present useful, in-depth introductions. CHARACTERISTIC CLASSES OF FOLIATIONS I. Bernshtein and B. Rosenfel'd In a recent article [1], Godbillon and Vey constructed a certain element ~ E H ~p÷~ (M, e) for an orienta- ble foliation ~r of codimension p on a manifold M* They showed also, that in the case p = 1 the class is related to the c0homologies of the Lie algebra of formal.

A construction of secondary characteristic classes of families of such foliations is also included. By means of these classes, new proofs of the rigidity of the Godbillon–Vey class in the category of transversely holomorphic foliations are given.

A Fête of Topology: Papers Dedicated to Itiro Tamura focuses on the progress in the processes, methodologies, and approaches involved in topology, including foliations, cohomology, and surface bundles. The publication first takes a look at leaf closures in Riemannian foliations and differentiable singular cohomology for foliations.

In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded subspace R equivalence classes are called the leaves of the foliation.

The purpose of this paper is to both survey and offer some new results on the non-triviality of the characteristic classes of Riemannian foliations.

We give examples where the primary Pontrjagin classes are all linearly independent. The independence of the secondary classes is also discussed, along with their total variation.An excerpt from the book Loop Spaces, Characteristic Classes and Geometric Quantization by Jean-Luc Brylinski is mentioned below: Characteristic classes are certain cohomology classes associated ential-geometry characteristic-classes connections derham-cohomology.Segal Classifying spaces related to foliations.

() 2 Introduction to Godbillon-Vey Classes De nition. Thurstons example that G-V is a continuous class (explained very well in Moritas book). Botts examples. References: Morita: Geometry of characteristic classes (book). Bott: Lectures on characteristic classes and foliations Harsh V Pittie.