Almost-Bieberbach Groups: Affine and Polynomial Structures
Almost-Bieberbach Groups: Affine and Polynomial Structures
Springer | December 5, 1996 | ISBN-10: 3540618996 | 259 pages | PDF | 8.31 mb
Springer | December 5, 1996 | ISBN-10: 3540618996 | 259 pages | PDF | 8.31 mb
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.