Almost-Bieberbach Groups: Affine and Polynomial Structures
Starting from basic knowledge of nilpotent (Lie) groups, an algebraic theory of almost-Bieberbach groups, the fundamental groups of infra-nilmanifolds, is developed. These are a natural generalization of the well known Bieberbach groups and many results a
- PDF / 10,964,744 Bytes
- 267 Pages / 432 x 666 pts Page_size
- 110 Downloads / 204 Views
1639
S rin er
BPerlin g Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore
Tokyo
Karel Dekimpe
Almost-Bieberbach Groups: Affine and Polynomial Structures
Springer
Author Karel Dekimpe* Katholieke Universiteit Leuven Campus Kortrijk Universitaire Campus B-8500 Kortrijk, Belgium e-mail: Karel.Dekimpe @ kulak.ac.be * Postdoctoral Fellow of the Belgian National Fund for Scientific Research (N.EWO.)
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Dekimpe, Karel:
Almost Bieberbach groups: affine and polynomial structures / Karel Dekimpe. - Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo S 9 p r i n g e r , 1996 (Lecture notes in mathematics ; 1639) ISBN 3-540-61899-6 NE: GT Mathematics Subject Classification (1991): Primary: 20H15, 57S30 Secondary: 20F18, 22E25 ISSN 0075-8434 ISBN 3-540-61899-6 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. 9Springer-Verlag Berlin Heidelberg 1996 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10479900 46/3142-543210 - Printed on acid-free paper
For Katleen, Charlotte and Sofie.
Preface The reader taking a first glance at this monograph nfight have the (wrong) impression that a lot of t o p o l o g y / g e o m e t r y is involved. Indeed, the objects we study in this book are a special kind of manifold, called the infra-nilmanifolds. This is a class of manifolds that can, and should, be viewed as a generalization of the flat Riemarmian manifolds. However, the reader fa,*niliar with the theory of the fiat Riemannian manifolds knows that such a manifold is completely determined by its fundamental group. Moreover, the groups that occur as such a fundamental group can be characterized in a purely algebraic way. More precisely, a group E is the fundamental group of a flat Riemannian manifold if and only if E is a finitely generated torsion free group containing a normal abelian subgroup of finite index. These groups are called Bieberbach groups. It follows that one can study the fiat Riemannian manifolds in a purely algebraic way. This group theoretical
Data Loading...
