Homology Theory An Introduction to Algebraic Topology [Paperback]

This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject.This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.General Introduction; Part I. Homology Theory of Polyhedra: 1. Background to Part I; 2. The Topology of Polyhedra; 3. Homology Theory of Simplicial Complex; 4. Chain Complexes; 5. The Contrahomology Ring for Polyhedra; 6. Abelian Groups and Homological Algebra; 7. The Fundamental Group and Covering Spaces; Part II. General Homology Theory; 8. Background to Part II; 9. Contrahomology and Maps; 10. Singular Homology Theory; 11. The Singular Contrahomology Ring; 12. Special Homology Theory and Homology Theory of Groups; Bibliography; Index.'This book achieves the purpose of providing an introduction which reaches the developing parts of the subject, and for those who already know a little algebraic topology is by far the best textbook for further study.' D.G. Palmer in Proceedings of the Edinburgh Mathematical Society'This is a badly needed book. It does an excellent job of carrying the serious beginning student of algebraic topology to a genuine acquaintance with the l3K