The Selected Works of J. Frank Adams, Volume 1

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Cambridge University Press, Oct 7, 1992 - Mathematics - 552 pages
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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 Few of them have been superseded by later work.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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Contents

Introduction page
xi
Introduction page
xiii
Maps between classifying spaces of compact Lie groups
xv
The cobar construction the Adams spectral sequence higher order
305
On the cobar construction
27
Chern characters revisited and addendum 24
29
On the structure and applications of the Steenrod algebra
34
Hopf algebras of cooperations for real and complex theory
36
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
Finite spaces and Lie groups
235
On the groups JX II
237
Spin8 triality F4 and all that
243
The fundamental representations of Es
254

Operations of the nth kind in theory
60
On the nonexistence of elements of Hopf invariant one
69
Stable operations on complex Ktheory
73
Modules over the Steenrod algebra and their Ext groups
87
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
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
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
2Tori in EK 264
367
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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Page 535 - MF Atiyah, K-theory and reality, Quart. J. Math. Oxford Ser. (2) 17 (1966), 367-386. MR 34 #6756.
Page 535 - MF Atiyah and R. Bott, On the periodicity theorem for complex vector bundles, Acta Math.

About the author (1992)

J. Peter May is professor of mathematics at the University of Chicago.

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