Author	Dekimpe, Karel. author
Title	Almost-Bieberbach Groups: Affine and Polynomial Structures [electronic resource] / by Karel Dekimpe
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1996
Connect to	http://dx.doi.org/10.1007/BFb0094472
Descript	X, 262 p. online resource

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

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

1. Mathematics
2. Group theory
3. Differential geometry
4. Mathematics
5. Group Theory and Generalizations
6. Differential Geometry