UID:
almahu_9949698056802882
Format:
1 online resource (xiii, 347 pages) :
,
illustrations, diagrams
ISBN:
1-281-76366-7
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9786611763664
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0-08-087316-2
Series Statement:
Pure and applied mathematics ; 8
Content:
Homotopy theory
Note:
Description based upon print version of record.
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Front Cover; Homotopy Theory, Volume 8; Copyright Page; Contents; PREFACE; LIST OF SPECIAL SYMBOLS AND ABBREVIATIONS; CHAPTER I. MAIN PROBLEM AND PRELIMINARY NOTIONS; 1. Introduction; 2. The extension problem; 3. The method of algebraic topology; 4. The retraction problem; 5. Combined maps; 6. Topological identification; 7. The adjunction space; 8. Homotopy problem and classification problem; 9. The homotopy extension property; 10. Relative homotopy; 11. Homotopy equivalences; 12. The mapping cylinder; 13. A generalization of the extension problem; 14. The partial mapping cylinder
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15. The deformation problem; 16. The lifting problem; 17. The most general problem; Exercises; CHAPTER II. SOME SPECIAL CASES OF THE MAIN PROBLEMS; 1. Introduction; 2. The exponential map p: R ? S1; 3. Classification of the maps S1 ? S1; 4. The fundamental group; 5. Simply connected spaces; 6. Relation between p1(X, x0) and H1 ( X ); 7. The Bruschlinsky group; 8. The Hopf theorems; 9. The Hurewicz theorem; Exercises; CHAPTER III. FIBER SPACES; 1. Introduction; 2. Covering homotopy property; 3. Definition of fiber space; 4. Bundle spaces; 5. Hopf fiberings of spheres
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6. Algebraically trivial maps X ? S27. Liftings and cross-sections; 8. Fiber maps and induced fiber spaces; 9. Mapping spaces; 10. The spaces of paths; 11. The space of loops; 12. The path lifting property; 13. The fibering theorem for mapping spaces; 14. The induced maps in mapping spaces; 15. Fiberings with discrete fibers; 16. Covering spaces; 17. Construction of covering spaces; Exercises; CHAPTER IV. HOMOTOPY GROUPS; 1. Introduction; 2. Absolute homotopy groups; 3. Relative homotopy groups; 4. The boundary operator; 5. Induced transformations; 6. The algebraic properties
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7. The exactness property; 8. The homotopy property; 9. The fibering property; 10. The triviality property; 11. Homotopy systems; 12. The uniqueness theorem; 13. The group structures; 14. The role of the basic point; 15. Local system of groups; 16. n-Simple spaces; Exercises; CHAPTER V. THE CALCULATION OF HOMOTOPY GROUPS; 1. Introduction; 2. Homotopy groups of the product of two spaces; 3. The one-point union of two spaces; 4. The natural homomorphisms from homotopy groups to homology groups; 5. Direct sum theorems; 6. Homotopy groups of fiber spaces; 7. Homotopy groups of covering spaces
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8. The n-connective fiberings; 9. The homotopy sequence of a triple; 10. The homotopy groups of a triad; 11. Freudenthal's suspension; Exercises; CHAPTER VI. OBSTRUCTION THEORY; 1. Introduction; 2. The extension index; 3. The obstruction cn+1 (g); 4. The difference cochain; 5. Eilenberg's extension theorem; 6. The obstruction sets for extension; 7. The homotopy problem; 8. The obstruction dn(f, g; ht); 9. The group Rn(K,L; f); 10. The obstruction sets for homotopy; 11. The general homotopy theorem; 12. The classification problem; 13. The primary obstructions; 14. Primary extension theorems; 15. Primary homotopy theorems
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English
Additional Edition:
ISBN 0-12-358450-7
Language:
English
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