Almost-Bieberbach Groups: Affine and Polynomial Structures

Karel Dekimpe3540618996, 9783540618997

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.

---

Table of contents :
front-matter……Page 1
1Preliminaries and notational conventions……Page 10
2Infra-nilmanifolds and Almost-Bieberbach groups……Page 21
3Algebraic characterizations of almost-crystallographic groups……Page 39
4Canonical type representations……Page 55
5The Cohomology of virtually nilpotent groups……Page 111
6Infra-nilmanifolds and their topological invariants……Page 129
7Classification survey……Page 166
back-matter……Page 238