Algebraic topology : a student's guide /

This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Adams, J. Frank (John Frank)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge [England] : University Press, 1972.
Colección:London Mathematical Society lecture note series ; 4.
Temas:
Algebraic topology.
Topologie algébrique.
MATHEMATICS > Topology.
Algebraic topology
Algebraische Topologie
Algebraïsche topologie.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 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
  • 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 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
  • 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

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