Download or read book Almost-Bieberbach Groups: Affine and Polynomial Structures written by Karel Dekimpe and published by Springer. This book was released on 2006-11-14 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.