Title: Almost-Bieberbach groups
First published: 1996
Description: 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.
Subjects: Topological transformation groups, Linear algebraic groups, Nilpotent groups, Algebras, linear, Group theory, Mathematics, Global differential geometry
LC classification: QA3 .L28 no. 1639, QA179 .L28 no. 1639