Algebraic Topology : A Student's Guide
J. F. Adams
Bok Engelsk 1972 · Electronic books.
| Annen tittel | |
|---|---|
| Utgitt | Cambridge , 1972
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| Omfang | 1 online resource (308 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Title; Copyright; Contents; Introduction; 1 A first course; 2 Categories and functors; 3 Semi-simplicial complexes; 4 Ordinary homology and cohomology; 5 Spectral sequences; 6 H*(BG); 7 Eilenberg-MacLane spaces and the Steenrod algebra; 8 Serrefs theory of classes of abelian groups (C-theory); 9 Obstruction theory; 10 Homotopy theory; 11 Fibre bundles and topology of groups; 12 Generalised cohomology theories; 13 Final touches; PAPERS ON ALGEBRAIC TOPOLOGY; 1; 1COMBINATORIAL HOMOTOPY; 4. Cell complexes.; 5. CW-complexes,; REFERENCES; 2; 2 AXIOMATIC APPROACH TO HOMOLOGY THEORY. - 1. Introduction2. Preliminaries; 3. Basic Concepts; 4. Axioms; 6. Existence; 7. Generalizations; 3&4; 3 LA SUITE SPECTRALE. I: CONSTRUCTION GENERALE; 1. Fondations; 2. Les suite f ondamentales; 3. Le cas gradue; 4. Le cas contravariant; 5. Le cas algebrique; 4 EXACT COUPLES IN ALGEBRAIC TOPOLOGY; Introduction; 1. Differential Groups; 2. Graded and Bigraded Groups; 3. Definition of a Leray-Koszul Sequence; 4. Definition of an Exact Couple; The Derived Couple; 5. Maps of Exact Couples; 6. Bigraded Exact Couples; The Associated Leray-Koszul Sequence; BIBLIOGRAPHY; 5. - 13 GENERALISED HOMOLOGY AND COHOMOLOGY THEORIES14; 14 Matematisk Institut, Aarhus Universitet; 1. Homology theories; 2. h-fibrations and their spectral sequence; 3. The case π = id: B - B; 4. Multiplicative cohomology theories; REFERENCES; 15,16&17; 15 ON AXIOMATIC HOMOLOGY THEORY; 16CHARACTERS AND COHOMOLOGY OF FINITE GROUPS; 3. Inverse limits and completions.; 17EXTRACT FROM THESIS; 18; 18 RELATIONS BETWEEN COHOMOLOGY THEORIES; Poincare duality; REFERENCES; 19,20,21 &22; 19VECTOR BUNDLES AND HOMOGENEOUS SPACES; 1. A cohomology theory derived from the unitary groups.. - 2. The spectral sequence.3. The differentiable Riemann-Roch theorem and some applications.; 4. The classifying space of a compact connected Lie group.; REFERENCES; 20 LECTURES ON K-THEORY; 1. Vector bundles on X and vector bundles on X x S; 2. Definition of K(X); 3. Proof of Bott periodicity; 4. Elements of Hopf invariant one; 21 VECTOR FIELDS ON SPHERES; 22 ON THE GROUPS J(X)-IV; 1. INTRODUCTION; 2. COF1BERINGS; 3. DEFINITION AND ELEMENTARY PROPERTIES OF THE INVARIANTS d, e; 12. EXAMPLES; REFERENCES; 23; 23A SUMMARY ON COMPLEX COBORDISM; 24. - 24NEW IDEAS IN ALGEBRAIC TOPOLOGY(K-THEORY AND ITS APPLICATIONS). - 5 THE COHOMOLOGY OF CLASSIFYING SPACES OF tf-SPACES6; 6 Cohomologie modulo 2 des complexes d'Eilenberg-MacLane; Introduction; 1. PrGlirninaires; 2. Determination de Palgfcbre #*(77; q,Z2); 4. Operations cohomologiques; BIBLIOGRAPHIE; 7; 7 ON THE TRIAD CONNECTIVITY THEOREM; 8&9; 8 ON THE FREUDENTHAL THEOREMS; 1. Introduction; BIBLIOGRAPHY; 9 THE SUSPENSION TRIAD OF A SPHERE; 1. Introduction; BIBLIOGRAPHY; 10; 10 ON THE CONSTRUCTION FK; 1. Introduction; 2. The construction; 3. A theorem of Hilton; References; 11; 11ON CHERN CHARACTERS AND THE STRUCTURE OF THEUNITARY GROUP; 12; 13. - This set of notes is aimed at graduate students who are specializing in algebraic topology.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 0521080762
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