Almost-Bieberbach Groups: Affine and Polynomial Structures / by Karel Dekimpe.

Format:

Book

Author/Creator:

Dekimpe, Karel, 1967- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1639.

Lecture Notes in Mathematics, 0075-8434 ; 1639

Language:

English

Subjects (All):

Group theory.

Global differential geometry.

Group Theory and Generalizations.

Differential Geometry.

Local Subjects:

Group Theory and Generalizations.

Differential Geometry.

Physical Description:

1 online resource (X, 262 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1996.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540495642

Access Restriction:

Restricted for use by site license.