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.

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Bibliographic Information

Book Title: Almost-Bieberbach Groups: Affine and Polynomial Structures
Authors: Karel Dekimpe
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0094472
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1996
Softcover ISBN: 978-3-540-61899-7Published: 18 November 1996
eBook ISBN: 978-3-540-49564-2Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 262
Topics: Group Theory and Generalizations, Differential Geometry

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Table of contents (7 chapters)

Front Matter

Preliminaries and notational conventions

Infra-nilmanifolds and Almost-Bieberbach groups

Algebraic characterizations of almost-crystallographic groups

Canonical type representations

The Cohomology of virtually nilpotent groups

Infra-nilmanifolds and their topological invariants

Classification survey

Back Matter

About this book