## Cohomology Operations |

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### Contents

PREFACE v | 1 |

The Dual of the Algebra d2 | 16 |

Embeddings of Spaces in Spheres | 30 |

6 other sections not shown

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abelian group acyclic complex Adem relations admissible monomials admissible sequences algebraic triples automorphism axioms binomial coefficient Cartan formula chain complex chain map Chapter cochain cocycle cohomology classes cohomology groups cohomology operations commutative diagram completes the proof continuous map COROLLARY cross-product cup-product CW complex define definition denote diagonal map dimension dual element embedding epimorphism equivariant chain map equivariant homotopy exterior algebra fibration fibre finite regular cell ft(p geometric triples Gn(q graded module homology homomorphism homotopy equivalent Hopf algebra Hopf invariant induces a map isomorphism Kp)p LEMMA lemma follows Let f map f map of geometric Math minimal carrier monomorphism non-zero normal cell obtain pairs permutation Pontrjagin ring projective space proposition proves the lemma q is odd reduced powers regular cell complex Sn_1 Sp(n Steenrod algebra Stiefel manifolds subcomplex subgroup Suppose tt-free vertical maps