Commutator calculus and groups of homotopy classes

CONTENTS\0......Page 5
Introduction to Part B\0......Page 7
Introduction to Part A\0......Page 15
Part A: Homotopy operations, nilpotent group theory and nilpotent Lie algebra theory\0......Page 0
1 The exponential function and the Zassenhaus formula\0......Page 20
2 The exponential commutator\0......Page 28
3 A presentation for the exponential group\0......Page 32
4 The general type of Zassenhaus terms and its characterization modulo a prime\0......Page 35
II. Distributivity laws in homotopy theory\0......Page 41
1 Whitehead products and cup products\0......Page 42
2 Hopf invariants\0......Page 48
3 The Whitehead product of composition elements\0......Page 55
4 Proof of I (1. 13) and I (2. 6)\0......Page 63
5 Decomposition of suspensions and groups of homotopy classes\0......Page 67
1 Spherical Whitehead products and commutators\0......Page 74
2 Spherical Hopf invariants\0......Page 77
3 Deviation from commutativity of spherical cup products\0......Page 81
4 Cup products of spherical Hopf invariants\0......Page 84
5 Hopf invariants of a Hopf invariant, of a sum and of a cup product\0......Page 89
6 Hopf invariant of a composition element\0......Page 91
1 Fxamples of higher order Hopf invariants on spheres\0......Page 97
2 Proof of theorem (1. 3)\0......Page 100
3 Zassenhaus terms for an odd prime\0......Page 104
0 Notation\0......Page 107
1 The homotopy Lie algebra and the spherical cohomotopy algebra\0......Page 109
2 Homotopy groups of spheres and homotopy coefficients\0......Page 114
3 The Hurewicz and the degree map\0......Page 119
1 Nilpotent rational groups of homotopy classes\0......Page 128
2 The exponential group\0......Page 130
3 Groups of homotopy classes\0......Page 132
4 H-maps and Co-H-maps\0......Page 137
1 The category of coefficients\0......Page 141
2 Extension of algebras by homotopy coefficients\0......Page 145
3 The extension of Lie algebras by homotopy coefficients\0......Page 150
4 The Hilton-Milnor theorem and its dual\0......Page 156
Literature\0......Page 162
Index\0......Page 165