Introduction to the Geometry of Foliation, Part B Foliations of Codi
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I ntroduction to the Geometry of Foliations, Part B
Aspect d Mathermtics Aspekte der Mathematik Editor: Klas Diederich
Vol. El: G. Hector/U. Hirsch, Introduction to the Geometry of Foliations, Part A Vol. E2: M. Knebusch/M. Kolster, Wittrings Vol. E3: G. Hector/U. Hirsch, Introduction to the Geometry of Foliations, Part B Vol. E4:
M. Laska, Elliptic Curves over Number Fields with Prescribed Reduction Type
The texts published in this series are intended for graduate students and all mathematicians who wish to broaden their research horizons or who simply want to get a better idea of what is going on in a given field. They are introductions to areas close to modern research at a high level and prepare the reader for a better understanding of research papers. Many of the books can also be used to supplement graduate course programs. The series will comprise two sub-series, one with English texts only and the other in German.
Gilbert Hector Ulrich Hirsch
Introduction to the Geometry of Foliations, Part B Foliations of Codimension One
Friedr. Vieweg & Sohn
BraunschweiglWiesbaden
CIP-Kurztitelaufnahme der Deutschen Bibliothek
Hector, Gilbert:
Hector, Gilbert:
Ulrich Hir.sch. - Braunschweig; Wiesbaden: Vieweg, 1983. (Introduction to the geometry of foliationsl Gilbert Hector; Ulrich Hirsch; Pt. B.I Aspects of mathematics; Vol. 3)
Foliations of codimension one/Gilbert Hector;
Introduction to the geometry of foliationsl Gilbert Hector; Ulrich Hirsch. - Braunschweig; Wiesbaden: Vieweg
(Aspects of mathematics; .. .1 NE: Hirsch, Ulrich
NE: Hirsch, Ulrich:; GT Pt. B. - Hector, Gilbert: Foliations of codimension
one
Dr. Gilbert Hector is Professor of Mathematics at the Universite des Sciences et Techniques de Lille I, France. Dr. Ulrich Hirsch is Professor of Mathematics at the University of Bielefeld, Germany.
1983 All rights reserved © Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig 1983 No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the copyright holder. Produced by IVD, Walluf b. Wiesbaden
ISBN-13: 978-3-528-08568-1 DOl: 10.1007/978-3-322-85619-7
e-ISBN-13: 978-3-322-85619-7
PRE F ACE
Part B of our Introduction to the Geometry of Foliations is a direct continuation of Part A (chapters 1- III) which has been published in the Aspects of Mathematics in 1981. In chapter I the study of foliations was carried out for surfaces. The object of Part B is to extend this to foliations of codimansion one on manifolds of arbitrary dimension. It will turn out that many of the phenomena we have observed on surfaces depend only on the codimension and thus have an analogue in codimension-one foliations on manifolds of higher dimension. Also the methods used to investigate foliated surfaces, for example gluing or turbulizing foliations, generalize directly to the higher dimensional case. They do not, however, suffice to provide a topological cla
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