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The Selected Works of J. Frank Adams

The Selected Works of J. Frank Adams
2 Volume Paperback Set


  • Date Published: November 2010
  • availability: Temporarily unavailable - available from TBC
  • format: Multiple copy pack
  • isbn: 9780521182140

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About the Authors
  • J. Frank Adams, one of the world's leading topologists, solved a number of celebrated problems in algebraic topology, a subject in which he initiated many of the most active areas of research. His papers written between 1955 and 1988, few of which have been superseded, are characterised by elegant writing and depth of thought. These two 1992 volumes contain all his major research contributions. The first contains papers on: the cobar construction, the Adams spectral sequence, higher-order cohomology operations, and the Hopf invariant one problem, amongst other topics. 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; and maps between classifying spaces of compact groups. Anyone interested in algebraic topology will want to own a copy of these volumes as a historical record and a source of reference.

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    Product details

    • Date Published: November 2010
    • format: Multiple copy pack
    • isbn: 9780521182140
    • length: 1097 pages
    • dimensions: 250 x 320 x 70 mm
    • weight: 2.3kg
    • availability: Temporarily unavailable - available from TBC
  • Table of Contents

    Volume 1:
    1. On the chain algebra of a loop space
    2. On the cobar construction
    3. The structure of the Steenrod algebra
    4. On the non-existence theory of elements of Hopf invariant one
    4. Applications of the Groethendieck–Atiyah–Hirzebruch functor K(X)
    5. Vector fields on spheres
    6. On complex Stiefel manifolds
    7. On matrices whose real linear combinations are non-singular and correction
    8. On the groups J(X) I, II, III, and IV and correction
    9. K-theory and the Hopf invariant
    10. Geometric dimension of bundles over RPn
    11. Lectures on generalised cohomology
    12. Algebraic topology in the last decade. Volume 2:
    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.

  • Editors

    Charles B. Thomas

    J. Peter May

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