CONTENTS Preface i v I. Homolog y an d cohomolog y theorie s 1 1. Preliminarie s 2 2. Homolog y an d cohomolog y theorie s 6 3. Spectr a 1 2 4. Product s 1 7 5. Spanier-Whitehea d dualit y 2 0 6. Poincar e dualit y (internal ) 2 4 7. Poincar e dualit y (external ) , 2 5 II. Semi-simplicia l spectr a 2 7 1. Semi-simplicia l spectr a «.. . 28 2. Grou p spectr a 3 0 3- Homotop y 3 0 4. Th e reduce d joi n o f tw o spectr a 3 4 5. Convergen t functor s - 3 5 6. Higher-orde r homolog y operation s 3 6 1, Degree s o f orientabilit y o f manifold s 3 8 III. Homotop y group s o f sphere s 3 9 1. Th e Adam s spectra l sequenc e 3 9 2. Som e computation s wit h th e Adam s spectra l sequenc e 4 4 3. Som e polynomia l subalgebra s o f E AS) 4 5 4. Th e /-homomorphis m 4 6 5. Unstabl e Adam s spectra l sequence s 4 9 IV. Stabl e homotop y group s a s ovmodule s 5 1 1. Higher-orde r composition s (* T Toda brackets** ) 5 1 2. Tod a bracket s an d extension s 5 3 3. Freyd* s generatin g hypothesi s 5 5 V. Cohomolog y an d extension s 5 8 1. Ordinar y homolog y theor y 5 8 2. K-theor y ....6 2 Bibliography , 6 5 Tables 7 0 iii
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