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Full Description
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 Few of them have been superseded by later work.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.
Contents
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.
