Almost-Bieberbach groups
Subtitle: affine and polynomial structures
By: Karel Dekimpe.
Series: Lecture notes in mathematics ;; 1639; Lecture notes in mathematics (Springer-Verlag) ;; 1639.
Publisher: Springer
Published: 1996
Place of publication: New York
Language: eng
Number of pages: 259
Subjects: Linear algebraic groups; Topological transformation groups; Nilpotent groups
Description: 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.
Notes: Includes bibliographical references (p. 251-255) and index.