Almost-Bieberbach Groups: Affine and Polynomial Structures
Seiten
1996
|
1996
Springer Berlin (Verlag)
978-3-540-61899-7 (ISBN)
Springer Berlin (Verlag)
978-3-540-61899-7 (ISBN)
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.
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.
Erscheint lt. Verlag | 18.11.1996 |
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Reihe/Serie | Lecture Notes in Mathematics |
Zusatzinfo | X, 262 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 216 x 279 mm |
Gewicht | 355 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
Schlagworte | affine structure • Bieberbach Gruppen • group theory • Gruppe (Mathematik) • Lie groups • manifold • polynomial structure |
ISBN-10 | 3-540-61899-6 / 3540618996 |
ISBN-13 | 978-3-540-61899-7 / 9783540618997 |
Zustand | Neuware |
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