Book contents
- Frontmatter
- Contents
- INTRODUCTION
- PAPERS ON ALGEBRAIC TOPOLOGY
- 1 Combinatorial homotopy
- 2 An axiomatic approach to homology theory
- 3 La suite spectrale. 1: Construction générale
- 4 Exact couples in algebraic topology
- 5 The cohomology of classifying spaces of H-spaces
- 6 Cohomologie modulo 2 des complexes d'Eilenberg-MacLane
- 7 On the triad connectivity theorem
- 8 On the Freudenthal theorems
- 9 The suspension triad of a sphere
- 10 On the construction FK
- 11 On Chern characters and the structure of the unitary group
- 12 Espaces fibrés et groupes d'homotopie. I, II
- 13 Generalised homology and cohomology theories
- 14 Relations between ordinary and extraordinary homology
- 15 On axiomatic homology theory
- 16 Characters and cohomology of finite groups
- 17 Extract from thesis
- 18 Relations between cohomology theories
- 19 Vector bundles and homogeneous spaces
- 20 Lectures on K-theory
- 21 Vector fields on spheres
- 22 On the groups J(X). IV
- 23 Summary on complex cobordism
3 - La suite spectrale. 1: Construction générale
Published online by Cambridge University Press: 23 May 2010
- Frontmatter
- Contents
- INTRODUCTION
- PAPERS ON ALGEBRAIC TOPOLOGY
- 1 Combinatorial homotopy
- 2 An axiomatic approach to homology theory
- 3 La suite spectrale. 1: Construction générale
- 4 Exact couples in algebraic topology
- 5 The cohomology of classifying spaces of H-spaces
- 6 Cohomologie modulo 2 des complexes d'Eilenberg-MacLane
- 7 On the triad connectivity theorem
- 8 On the Freudenthal theorems
- 9 The suspension triad of a sphere
- 10 On the construction FK
- 11 On Chern characters and the structure of the unitary group
- 12 Espaces fibrés et groupes d'homotopie. I, II
- 13 Generalised homology and cohomology theories
- 14 Relations between ordinary and extraordinary homology
- 15 On axiomatic homology theory
- 16 Characters and cohomology of finite groups
- 17 Extract from thesis
- 18 Relations between cohomology theories
- 19 Vector bundles and homogeneous spaces
- 20 Lectures on K-theory
- 21 Vector fields on spheres
- 22 On the groups J(X). IV
- 23 Summary on complex cobordism
Summary
The next two pieces constitute an introduction to spectral sequences, which today form an almost indispensable part of the topologistTs tool kit. For applications of spectral sequences, see §§5–8, 10, 12 of the introduction. The only prerequisite for reading the exposé by Eilenberg is a familiarity with the axiomatic approach to homology theory (see §1 of the introduction). In the extract by Massey the possible applications are more varied; some familiarity with elementary homotopy theory would be useful.
Fondations
Nous considérerons un ensemble muni dTune relation d'ordre (partielle), notée A < B, qui est réflexive (A < A) et transitive (A < B et B < C entraînent A < C). On suppos era que V ensemble contient un plus petit élément, noté 0, et un plus grand élément, noté 1; on a done 0 < A < 1 pour tout A. Nous considérerons des paires (A, B) oú B < A, et nous ecrirons (A, B) < lorsque A < et B <. De méme, nous considérerons des triples (A, B, C) où C < B < A, et nous écrirons (A, B, C) < lorsque A < A B < B et C < C Le triple (A, B, 0) sera identifié à la paire (A, B), et la paire (A, 0) sera identifiée à l'élément A.
Nous supposerons quTa toute paire (A, B) l'on ait associe un groupe abélien (ou un module sur un anneau), noté H(A, B), qu'à toute inégalité (A, B) < (A, B) I'on ait associé un homomorphisme H(A, B) → H(A, B), et qu'à tout triple (A, B, C) l'on ait associe un homomorphisme d: H(A, B) → H(B, C).
- Type
- Chapter
- Information
- Algebraic TopologyA Student's Guide, pp. 51 - 65Publisher: Cambridge University PressPrint publication year: 1972