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
12 - Espaces fibrés et groupes d'homotopie. I, II
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 paper, by Cartan and Serre, are the first announcement of the results of the French school on the method of killing homotopy groups (see §10). The end of the second note gives the flavour of practical calculations; the desire to be able to make calculations is important for motivation in this area. The prerequisites are a knowledge of elementary homotopy theory and of homology theory up to spectral sequences (see §§1, 4, 5 of the introduction).
TOPOLOGIE. – Espaces fibrés et groupes d'homotopie. I. Constructions générates. Note de MM. Henri Cartan et Jean-Pierre Serre, présentée par M. Jacques Hadamard.
Construction d'espaces fibrés (1) permetlant de le groupe d'homotopie πn(X) d'un espace X dont les πt(X) sont nuls pour i < n. Gette methode généralise celle qui consiste, pour n = 1, lorsque X est connexe, le groupe fondamental πt(X) en passant au revetement universel de X.
1. Soient X un espace connexe par arcs, x∈X, S(X) le complexe singulier de X. Pour tout entier q≥1, soit e>(X; x, q) le sous-complexe engendré par les simplexes dont les (q– I)-faces sont en x. Les groupes d'homologie (resp. cohomologie) de S(X; x, q) à coefficients dans G sont les groupes d'Eilenberg (2) de l'espace X en x; on les notera Hi(X; x, q, G), resp. Hi(X; x, q, G).
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- Algebraic TopologyA Student's Guide, pp. 140 - 145Publisher: Cambridge University PressPrint publication year: 1972