The Selected Works of J. Frank Adams

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

• ISBN13: 9780521110686
• ISBN10: 0521110688
• Edition: 1st
• Format: Paperback
• Copyright: 2010-01-14
• Publisher: Cambridge University Press

Summary

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 Few of them have been superseded by later work.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.

Table of Contents

On formulae of Thom and Wu

On Chern characters and the structure of the unitary group

Chern characters revisited and the structure of the unitary group

Chern characters revisited and addendum

The Hurewicz homomorphism for MU and BP

Hopf algebras of co-operators for real and complex K-theory

Operations of the Nth kind in K-theory

Operations on K-theory of torsion-free spaces

Stable operations on complex K-theory

Primitive elements in the K-theory of BSU

A finiteness theorem in homological algebra

A periodicity theorem in homological algebra

Modules over the Steenrod algebra

Sub-Hopf-algebras of the Steenrod algebra

What we don't know about RP+

Calculations of Lin's Ext groups

The Segal conjecture for elementary abelian p-groups

The sphere considered as an H-space mod p

H-spaces with few cells

Finite H-spaces and Lie groups

Spin(8) triality, F4 and all that

The fundamental representations of E8

2-tori in E8; Maps between classifying spaces I, II, and III

Maps between p-completed classifying spaces

An example in homotopy theory

A variant of E. H. Brown's representability theorem

Idempotent functors in homotopy theory

The Kahn-Priddy theorem

Uniquenesss of BSO

Graeme Segal's Burnsides ring conjecture

A generalisation of the Segal conjecture

A generalisation of the Atiyah-Segal completion theorem

Atomic spaces and spectra

Two theorems of

The work of

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