The Selected Works of J. Frank Adams: Volume 1

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)

9780521110679, Cambridge University Press

Paperback, published 14 January 2010

556 pages
24.6 x 18.9 x 2.9 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 Few of them have been superseded by later work.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 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.

Subject Areas: Algebraic topology [PBPD]