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Almost-Bieberbach Groups: Affine and Polynomial Structures

Karel Dekimpe, "Almost-Bieberbach Groups: Affine and Polynomial Structures"
2007 | pages: 267 | ISBN: 3540618996 | PDF | 6,7 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.

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Tags: Groups, Affine, Polynomial, Structures

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