The Selected Works of J. Frank Adams

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

• ISBN13: 9780521110679
• ISBN10: 052111067X
• Edition: 1st
• Format: Paperback
• Copyright: 2010-01-14
• Publisher: Cambridge University Press

Summary

This selection of Adams' work in two volumes brings together all his major research contributions. They are organized by subject matter rather than in strict chronological order. The first volume contains papers on the cobar construction, the Adams spectral sequence, higher order cohomology operations, and the Hopf invariant one problem, applications of K-theory, generalized 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, and maps between classifying spaces and compact groups.

Table of Contents

On the chain algebra of a loop space

On the cobar construction

The structure of the Steenrod algebra

On the non-existence theory of elements of Hopf invariant one

Applications of the Groethendieck-Atiyah-Hirzebruch functor K(X)

Vector fields on spheres

On complex Stiefel manifolds

On matrices whose real linear combinations are non-singular and correction

On the groups J(X) I, II, III, and IV and correction

K-theory and the Hopf invariant

Geometric dimension of bundles over RPn

Lectures on generalised cohomology

Algebraic topology in the last decade

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