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

Ulrich Hirsch

ISBN 10: 3322984834 / ISBN 13: 9783322984838

Edité par Vieweg+Teubner Verlag, 2012

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pion~er work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and W. Kaplan - to name a few - who all studied 'regular curve families' on surfaces, and later by Ch. Ehresmann, G. Reeb, A. Haefliger and ot'ners between 1940 and 1960. Since then the subject has developed from a collection of a few papers to a wide field of research. i~owadays, one usually distinguishes between two main branches of foliation theory, the so-called quantitative theory (including homotopy theory and characteristic classes) on the one hand, and the qualitative or geometric theory on the other. The present volume is the first part of a monograph on geometric aspects of foliations. Our intention here is to present some fundamental concepts and results as well 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 this goal has been achieved.

N° de réf. du vendeur 9783322984838

Détails bibliographiques

• Titre: Introduction to the Geometry of Foliations, Part A : Foliations on Compact Surfaces, Fundamentals for Arbitrary Codimension, and Holonomy
• Éditeur: Vieweg+Teubner Verlag
• Date de parution: 2012
• Langue: allemand
• ISBN à 10 chiffres: 3322984834
• ISBN à 13 chiffres: 9783322984838
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 244 L x 170 H x 14 P (en millimètres) 244 millimètres de largeur par 170 millimètres de hauteur par 14 millimètres de profondeur
• Poids: 442 grammes

A propos de ce titre

Synopsis

Foliation theory grew out of the theory of dynamical systems on manifolds and Ch. Ehresmann's connection theory on fibre bundles. Pion er work was done between 1880 and 1940 by H. Poincare, I. Bendixson, H. Kneser, H. Whitney, and W. Kaplan - to name a few - who all studied "regular curve families" on surfaces, and later by Ch. Ehresmann, G. Reeb, A. Haefliger and ot"ners between 1940 and 1960. Since then the subject has developed from a collection of a few papers to a wide field of research. i owadays, one usually distinguishes between two main branches of foliation theory, the so-called quantitative theory (including homotopy theory and characteristic classes) on the one hand, and the qualitative or geometric theory on the other. The present volume is the first part of a monograph on geometric aspects of foliations. Our intention here is to present some fundamental concepts and results as well 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 this goal has been achieved.