Invitation to Combinatorial Topology

An elementary text that can be understood by anyone with a background in high school geometry, Invitation to Combinatorial Topology offers a stimulating initiation to important topological ideas. This translation from the original French does full justice to the text's coherent presentation as well as to its rich historical content. Subjects include the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, reduction to normal form, and application to the geometric theory of functions. 1967 edition. 108 figures. Bibliography. Index.

ForewordTranslator's PrefaceCHAPTER ONE. TOPOLOGICAL GENERALITIES1. Qualitative Geometric Properties2. Coloring Geographical Maps3. The Problem of Neighboring Regions4. "Topology, India-Rubber Geometry"5. Homeomorphism6. "Topology, Continuous Geometry"7. "Comparison of Elementary Geometry, Projective Geometry, and Topology"8. Relative Topological Properties9. Set Topology and Combinatorial Topology10. The Development of TopologyCHAPTER TWO. TOPOLOGICAL NOTIONS ABOUT SURFACES11. Descartes' Theorem12. An Application of Descartes' Theorem13. Characteristic of a Surface14. Unilateral Surfaces15. Orientability and Nonorientability16. Topological Polygons17. Construction of Closed Orientable Surfaces from Polygons by Identifying Their Sides18. Construction of Closed Nonorientable Surfaces from Polygons by Identifying Their Sides19. Topological Definition of a Closed SurfaceCHAPTER THREE. TOPOLOGICAL CLASSIFICATION OF CLOSED SURFACES20. The Principle Problem in the Topology of Surfaces21. Planar Polygonal Schema and Symbolic Representation of a Polyhedron22. Elementary Operations23. Use of Normal Forms of Polyhedra24. Reduction to Normal Form: I25. Reduction to Normal Form: II26. Characteristic and Orientability27. The Principle Theorem of the Topology of Closed Surfaces28. Application to the Geometric Theory of Functions29. Genus and Connection Number of Closed Orientable SurfacesBibliographyTRANSLATOR'S NOTESIndex