The Selected Works of J. Frank Adams:

Couverture
Cambridge University Press, 7 oct. 1992 - 545 pages
J. Frank Adams was one of the world's leading topologists. He solved a number of celebrated problems in algebraic topology, a subject in which he initiated many of the most active areas of research. He wrote a large number of papers during the period 1955-1988, and they are characterised by elegant writing and depth of thought. Few of them have been superseded by later work. This selection, in two volumes, brings together all his major research contributions. They are organised by subject matter rather than in strict chronological order. The first contains papers on: the cobar construction, the Adams spectral sequence, higher-order cohomology operations, and the Hopf invariant one problem; applications of K-theory; generalised homology and cohomology theories. The second volume is mainly concerned with Adams' contributions to: characteristic classes and calculations in K-theory; modules over the Steenrod algebra and their Ext groups; finite H-spaces and compact Lie groups; maps between classifying spaces of compact groups. Every serious student or practitioner of algebraic topology will want to own a copy of these two volumes both as a historical record and as a source of continued reference.
 

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Table des matières

On Chern characters and the structure of the unitary group
13
On the cobar construction
27
The Hurewicz homomorphism for MU and BP
29
On the structure and applications of the Steenrod algebra
34
Operations of the nth kind in theory
60
Stable operations on complex Atheory
73
Primitive elements in the Ltheory of BSU 11
87
On the nonexistence of elements of Hopf invariant one 69
92
On the groups JXII
237
The fundamental representations of 8
254
On the groups JXIII
272
Maps between classifying spaces of compact Lie groups
275
On the groups JXIV and correction
302
Maps between classifying spaces II
316
theory and the Hopf invariant
354
Geometric dimension of bundles over RPn
362

Modules over the Steenrod algebra
106
What we dont know about RP
126
The Segal conjecture for elementary abelian pgroups
143
Applications of Atheory
154
Vector fields on spheres
161
Finite spaces and compact Lie groups
169
On complex Stiefel manifolds
191
On matrices whose real linear combinations are nonsingular
214
On the groups JX I
222
Finite spaces and algebras over the Steenrod algebra and correction
235
Generalised homology and cohomology theories and a survey
377
Maps between classifying spaces III
381
Maps between completed classifying spaces
399
Idempotent functors in homotopy theory
422
Uniqueness of BSO
440
Graeme Segals Burnside ring conjecture
475
A generalization of the AtiyahSegal completion theorem
500
Two unpublished expository papers
515
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