## Cohomology Operations, Issues 50-51Written and revised by D. B. A. Epstein. |

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### Contents

PREFACE | 1 |

The Dual of the Algebra 2 | 16 |

Embeddings of Spaces in Spheres | 30 |

The Cohomology of Classical Groups and Stiefel Manifolds | 37 |

Equivariant Cohomology | 58 |

Axiomatic Development of the Algebra ftp | 76 |

Construction of the Reduced Powers | 97 |

Relations of Adem and the Uniqueness Theorem | 115 |

Algebraic Derivations of Certain Properties of | 133 |

### Common terms and phrases

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 elements embedding epimorphism equivariant chain map equivariant homotopy exterior algebra fibration fibre finite regular cell ft(p geometric triples Gn(q graded module homomorphism homotopy equivalent Hopf algebra Hopf invariant Hurewicz theorem induces a map isomorphism K;Zp LEMMA lemma follows Let f map f map of geometric Math minimal carrier monomorphism non-zero normal cell obtain pairs permutation proposition proves the lemma q is odd reduced powers regular cell complex Sp(n Steenrod algebra Stiefel manifolds subcomplex subgroup Suppose vertical maps