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.
General
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