The Selected Works of J. Frank Adams

The selected works of one the greatest names in algebraic topology.

J. Frank Adams (Author), J. Peter May (Edited by), Charles B. Thomas (Edited by)

9780521110686, Cambridge University Press

Paperback, published 14 January 2010

548 pages
24.6 x 18.9 x 2.8 cm, 0.98 kg

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 Few of them have been superseded by later work.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.

1. On formulae of Thom and Wu
2. On Chern characters and the structure of the unitary group
3. Chern characters revisited and the structure of the unitary group
4. Chern characters revisited and addendum
5. The Hurewicz homomorphism for MU and BP
6. Hopf algebras of co-operators for real and complex K-theory
7. Operations of the Nth kind in K-theory
8. Operations on K-theory of torsion-free spaces
9. Stable operations on complex K-theory
10. Primitive elements in the K-theory of BSU
11. A finiteness theorem in homological algebra
12. A periodicity theorem in homological algebra
13. Modules over the Steenrod algebra
14. Sub-Hopf-algebras of the Steenrod algebra
15. What we don't know about RP?
16. Calculations of Lin's Ext groups
17. The Segal conjecture for elementary abelian p-groups
18. The sphere considered as an H-space mod p
19. H-spaces with few cells
20. Finite H-spaces and Lie groups
21. Spin(8) triality, F4 and all that
22. The fundamental representations of E8
23. 2-tori in E8
Maps between classifying spaces I, II, and III
24. Maps between p-completed classifying spaces
25. An example in homotopy theory
26. A variant of E. H. Brown's representability theorem
27. Idempotent functors in homotopy theory
28. The Kahn–Priddy theorem
29. Uniquenesss of BSO
30. Graeme Segal's Burnsides ring conjecture
31. A generalisation of the Segal conjecture
32. A generalisation of the Atiyah–Segal completion theorem
33. Atomic spaces and spectra
34. Two theorems of J. Lannes
35. The work of M. J. Hopkins.

Subject Areas: Algebraic topology [PBPD]