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Almost-Bieberbach Groups: Affine and Polynomial Structures / by Karel Dekimpe
(Lecture Notes in Mathematics. ISSN:16179692 ; 1639)
版 | 1st ed. 1996. |
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出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
出版年 | 1996 |
大きさ | X, 262 p : online resource |
著者標目 | *Dekimpe, Karel author SpringerLink (Online service) |
件 名 | LCSH:Group theory LCSH:Geometry, Differential FREE:Group Theory and Generalizations FREE:Differential Geometry |
一般注記 | 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 HTTP:URL=https://doi.org/10.1007/BFb0094472 |
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Springer eBooks | 9783540495642 |
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EB00210338 |
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