Author | Charlap, Leonard S. author |
---|---|
Title | Bieberbach Groups and Flat Manifolds [electronic resource] / by Leonard S. Charlap |
Imprint | New York, NY : Springer New York, 1986 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8687-2 |
Descript | XIII, 242 p. online resource |
I. Bierberbachโs Three Theorems -- 1. Rigid Motions -- 2. Examples -- 3. Bierberbachโs First Theorem -- 4. Bierberbachโs Second Theorem -- 5. Digression โ Group Extensions -- 6. Digression โ Integral Repesentations of Finite Groups -- 7. Bieberbachโs 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 โ Cohomology of Groups -- 4. Examples -- 5. Holonomy Groups -- IV. Holonomy Groups of Prime Order -- 1. Introduction -- 2. Digression โ 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