Almost-Bieberbach Groups: Affine and Polynomial Structures

  • Authors
  • Karel┬áDekimpe
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1639)

Table of contents

  1. Front Matter
    Pages I-X
  2. Karel Dekimpe
    Pages 1-11
  3. Karel Dekimpe
    Pages 47-102
  4. Karel Dekimpe
    Pages 103-120
  5. Karel Dekimpe
    Pages 159-230
  6. Back Matter
    Pages 231-259

About this book

Introduction

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 about ordinary Bieberbach groups turn out to generalize to the almost-Bieberbach groups. Moreover, using affine representations, explicit cohomology computations can be carried out, or resulting in a classification of the almost-Bieberbach groups in low dimensions. The concept of a polynomial structure, an alternative for the affine structures that sometimes fail, is introduced.

Keywords

Group theory Lie groups affine structure manifold polynomial structure

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0094472
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-61899-7
  • Online ISBN 978-3-540-49564-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book