The Selected Works of J. Frank Adams, Том 1

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Cambridge University Press, 7 жовт. 1992 р. - 552 стор.
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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 Few of them have been superseded by later work.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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Зміст

On the cobar construction
27
On the structure and applications of the Steenrod algebra
34
On the nonexistence of elements of Hopf invariant one
69
A periodicity theorem in homological algebra
93
Modules over the Steenrod algebra
106
SubHopfalgebras of the Steenrod algebra
118
What we dont know about RP
126
Calculation of Lins Ext groups
132
Finite spaces and Lie groups
235
On the groups JX II
237
Spin8 triality F4 and all that
243
The fundamental representations of 8
254
On the groups JXIII
272
On the groups JXIV and correction
302
Atheory and the Hopf invariant
354
Geometric dimension of bundles over RPn
362

The Segal conjecture for elementary abelian groups
143
Applications of Atheory
154
Vector fields on spheres
161
Finite spaces and compact Lie groups
169
spaces with few cells
178
Finite spaces and algebras over the Steenrod algebra and correction
184
On complex Stiefel manifolds
191
On matrices whose real linear combinations are nonsingular
214
On the groups JXI
222
Generalised homology and cohomology theories and a survey
377
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
Algebraic topology in the last decade
515
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Популярні уривки

Сторінка 535 - MF Atiyah, K-theory and reality, Quart. J. Math. Oxford Ser. (2) 17 (1966), 367-386. MR 34 #6756.
Сторінка 535 - MF Atiyah and R. Bott, On the periodicity theorem for complex vector bundles, Acta Math.

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