Bieberbach Groups and Flat Manifolds - Brossura

Charlap, Leonard S.

Brossura

ISBN 10: 0387963952 ISBN 13: 9780387963952

Casa editrice: Springer New York, 1986

Riassunto

A flat riemannian manifold is a space in which you can talk about geometry (e. In this book we are mainly concerned with compact flat riemannian manifolds, and unless we say otherwise, we use the term "flat manifold" to mean "compact flat riemannian manifold.

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Contenuti

I. Bierberbach’s Three Theorems.- 1. Rigid Motions.- 2. Examples.- 3. Bierberbach’s First Theorem.- 4. Bierberbach’s Second Theorem.- 5. Digression ― Group Extensions.- 6. Digression ― Integral Repesentations of Finite Groups.- 7. Bieberbach’s Third Theorem and Some Remarks.- II. Flat Riemannian Manifolds.- 1. Introduction.- 2. A Tiny Bit of Differential Topology.- 3. Connections and Curvature.- 4. Riemannian Structures.- 5. Flat Manifolds.- 6. Conjectures and Counterexamples.- III. Classification Theorems.- 1. The Algebraic Structure of Bieberbach Groups.- 2. A General Classification Scheme for Bieberbach Groups.- 3. Digression ― Cohomology of Groups.- 4. Examples.- 5. Holonomy Groups.- IV. Holonomy Groups of Prime Order.- 1. Introduction.- 2. Digression ― Some Algebraic Number Theory.- 3. Modules over the Cyclotomic Ring.- 4. Modules over Groups of Prime Order.- 5. The Cohomology of Modules over Groups of Prime Order.- 6. The Classification Theorem.- 7. ?p-manifolds.- 8. An Interesting Example.- 9. The Riemannian Structure of Some ?p manifolds.- V. Automorphisms.- 1. The Basic Diagram.- 2. The Hochschild-Serre Exact Sequence.- 3. 9-Diagrams.- 4. Automorphisms of Group Extensions.- 5. Automorphisms of Bieberbach Groups.- 6. Automorphisms of Flat Manifolds.- 7. Automorphisms of ?p-manifolds.

Product Description

Book by Charlap Leonard S

Dettagli dell'edizione

• Editore: Springer New York
• Data di pubblicazione: 1986
• Lingua: Inglese
• ISBN 10: 0387963952
• ISBN 13: 9780387963952
• Rilegatura: Copertina flessibile
• Numero di pagine: 260
• Contatto del produttore: non disponibile
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