General Cohomology Theory and K-Theory

P. J. Hilton

doi:10.1017/CBO9780511662577

These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences.

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General Cohomology Theory and K-Theory

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Contents

Frontmatter
pp i-ii

Contents
pp iii-iv

Introduction
pp 1-6

Chapter I - General Cohomology Theories
pp 7-16

Chapter II - Exact Couples and Spectral Sequences
pp 17-31

Chapter III - The Generalized Atiyah-Hirzebruch Spectral Sequence
pp 32-53

Chapter IV - K-Theory
pp 54-66

Chapter V - K-Theory, the Chern Character and the Hopf Invariant Problem
pp 67-81

Appendix: On the Construction of Cohomology Theories
pp 82-101

Bibliography
pp 102-102

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General Cohomology Theory and K-Theory

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