Almost-Bieberbach Groups: Affine and Polynomial Structures
Dekimpe, Karel.
Almost-Bieberbach Groups: Affine and Polynomial Structures [electronic resource] / by Karel Dekimpe. - X, 262 p. online resource. - Lecture Notes in Mathematics, 1639 0075-8434 ; . - Lecture Notes in Mathematics, 1639 .
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.
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.
9783540495642
10.1007/BFb0094472 doi
Group theory.
Global differential geometry.
Group Theory and Generalizations.
Differential Geometry.
QA174-183
512.2
Almost-Bieberbach Groups: Affine and Polynomial Structures [electronic resource] / by Karel Dekimpe. - X, 262 p. online resource. - Lecture Notes in Mathematics, 1639 0075-8434 ; . - Lecture Notes in Mathematics, 1639 .
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.
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.
9783540495642
10.1007/BFb0094472 doi
Group theory.
Global differential geometry.
Group Theory and Generalizations.
Differential Geometry.
QA174-183
512.2