Author | Fomenko, Anatolij T. author |
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Title | Visual Geometry and Topology [electronic resource] / by Anatolij T. Fomenko |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1994 |
Connect to | http://dx.doi.org/10.1007/978-3-642-76235-2 |
Descript | XVI, 324 p. 51 illus. online resource |
1 Polyhedra. Simplicial Complexes. Homologies -- 1.1 Polyhedra -- 1.2 Simplicial Homology Groups of Simplicial Complexes (Polyhedra) -- 1.3 General Properties of Simplicial Homology Groups -- 2 Low-Dimensional Manifolds -- 2.1 Basic Concepts of Differential Geometry -- 2.2 Visual Properties of One-Dimensional Manifolds -- 2.3 Visual Properties of Two-Dimensional Manifolds -- 2.4 Cohomology Groups and Differential Forms -- 2.5 Visual Properties of Three-Dimensional Manifolds -- 3 Visual Symplectic Topology and Visual Hamiltonian Mechanics -- 3.1 Some Concepts of Hamiltonian Geometry -- 3.2 Qualitative Questions of Geometric Integration of Some Differential Equations. Classification of Typical Surgeries of Liouville Tori of Integrable Systems with Bott Integrals -- 3.3 Three-Dimensional Manifolds and Visual Geometry of Isoenergy Surfaces of Integrable Systems -- 4 Visual Images in Some Other Fields of Geometry and Its Applications -- 4.1 Visual Geometry of Soap Films. Minimal Surfaces -- 4.2 Fractal Geometry and Homeomorphisms -- 4.3 Visual Computer Geometry in the Number Theory -- Appendix 1 Visual Geometry of Some Natural and Nonholonomic Systems -- 1.1 On Projection of Liouville Tori in Systems with Separation of Variables -- 1.2 What Are Nonholonomic Constraints? -- 1.3 The Variety of Manifolds in the Suslov Problem -- Appendix 2 Visual Hyperbolic Geometry -- 2.1 Discrete Groups and Their Fundamental Region -- 2.2 Discrete Groups Generated by Reflections in the Plane -- 2.3 The Gram Matrix and the Coxeter Scheme -- 2.4 Reflection-Generated Discrete Groups in Space -- 2.5 A Model of the Lobachevskian Plane -- 2.6 Convex Polygons on the Lobachevskian Plane -- 2.7 Coxeter Polygons on the Lobachevskian Plane -- 2.8 Coxeter Polyhedra in the Lobachevskian Space -- 2.9 Discrete Groups of Motions of Lobachevskian Space and Groups of Integer-Valued Automorphisms of Hyperbolic Quadratic Forms -- 2.10 Reflection-Generated Discrete Groups in High-Dimensional Lobachevskian Spaces -- References