Introduction to the Geometry of Foliations, Part A: Foliations on Compact Surfaces, Fundamentals for Arbitrary Codimension, and Holonomy (Aspects of Mathematics)

Gilbert Hector

ISBN 10: 3528185015 / ISBN 13: 9783528185015

Published by Vieweg+Teubner Verlag 1986-01-01, 1986

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Seller Inventory # 6666-IUK-9783528185015

Bibliographic Details

• Title: Introduction to the Geometry of Foliations, Part A: Foliations on Compact Surfaces, Fundamentals for Arbitrary Codimension, and Holonomy (Aspects of Mathematics)
• Publisher: Vieweg+Teubner Verlag 1986-01-01
• Publication Date: 1986
• Language: English
• ISBN 10: 3528185015
• ISBN 13: 9783528185015
• Binding: Paperback
• Edition: 2nd Edition
• Condition: New

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Synopsis

Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pioneer work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and IV. Kaplan - to name a few - who all studied "regular curve families" on surfaces, and later by Ch. Ehresmann, G. Reeb, A. Haefliger and otners between 1940 and 1960. Since then the subject has developed from a collection of a few papers to a wide field of research. owadays, one usually distinguishes between two main branches of foliation theory, the so-called quantitative theory (including homotopy theory and cnaracteristic classes) on the one hand, and the qualitative or geometrie theory on the other. The present volume is the first part of a monograph on geometrie aspects of foliations. Our intention here is to present some fundamental concepts and results as weIl as a great number of ideas and examples of various types. The selection of material from only one branch of the theory is conditioned not only by the authors' personal interest but also by the wish to give a systematic and detailed treatment, including complete proofs of all main results. We hope that tilis goal has been achieved.