Almost-Bieberbach Groups: Affine and Polynomial Structures

Karel Dekimpe (Autor)

Buch | Softcover

X, 262 Seiten

1996
Springer Berlin (Verlag)
978-3-540-61899-7 (ISBN)

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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
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