Almost-Bieberbach Groups Affine and Polynomial Structures |
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| Author:
| Dekimpe, Karel |
| Series title: | Lecture Notes in Mathematics Ser. |
| ISBN: | 978-3-540-61899-7 |
| Publication Date: | Nov 1996 |
| Publisher: | Springer Berlin / Heidelberg
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| Imprint: | Springer |
| Book Format: | Paperback |
| List Price: | USD $69.95USD $69.95 |
Book Description:
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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...
More DescriptionStarting 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.