Algebraic TopologyCourier Corporation, 1 janv. 1996 - 375 pages Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal for a course on either homotopy or homology theory.The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope that they have a better chance of solution. The translation process is usually carried out by means of the homology or homotopy groups of a topological space. Much of the book is therefore concerned with the construction of these algebraic invariants, and with applications to topological problems, such as the classification of surfaces and duality theorems for manifolds. Other important topics covered are homotopy theory, CW-complexes and the co-homology groups associated with a general Ω-spectrum.Dr. Maunder has provided many examples and exercises as an aid, and the notes and references at the end of each chapter trace the historical development of the subject and also point the way to more advanced results."Throughout the text the style of writing is first class. The author has given much attention to detail, yet ensures that the reader knows where he is going. An excellent book." -- Bulletin of the Institute of Mathematics and Its Applications. |
Table des matières
Introduction | 1 |
HOMOTOPY AND SIMPLICIAL COMPLEXES | 23 |
1 | 63 |
31 | 99 |
63 | 123 |
71 | 139 |
87 | 157 |
Exercises | 173 |
Notes on Chapter 3 | 199 |
GENERAL HOMOTOPY THEORY | 200 |
1 | 205 |
Introduction | 257 |
CHAPTER 8 | 311 |
| 361 | |
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Expressions et termes fréquents
1-1)-correspondence AH'I algebraic base point based map boundary chain complex chain map Chapter coefficients cofibre cofibre map cohomology commutative diagram composite constant map construct contained continuous map Corollary corresponding CW-complex defined Definition disjoint union element exact sequence example Exercise exists fibre map follows free abelian group Given H-space Hausdorff Hence homeomorphic homology groups homology n-manifold homotopy classes homotopy equivalence homotopy extension property homotopy F identification map identified identity map inclusion map induces integer inverse isomorphism Let f manifolds map f map ƒ map g map of pairs Moreover n-simplex open set path-connected polyhedra polyhedron Proof properties Proposition prove result Similarly simplex simplicial approximation Simplicial Approximation Theorem simplicial complex simplicial map space obtained subcomplex subset subspace theory topological space topology triangulation vertex vertices X₁ Y₁ Z₂