## The Selected Works of J. Frank Adams, Volume 1J. Frank Adams was one of the world's leading topologists. He solved a number of celebrated problems in algebraic topology, a subject in which he initiated many of the most active areas of research. He wrote a large number of papers during the period 1955–1988, and they are characterised by elegant writing and depth of thought. Few of them have been superseded by later work. This selection, in two volumes, brings together all his major research contributions. They are organised by subject matter rather than in strict chronological order. The first contains papers on: the cobar construction, the Adams spectral sequence, higher-order cohomology operations, and the Hopf invariant one problem; applications of K-theory; generalised homology and cohomology theories. The second volume is mainly concerned with Adams' contributions to: characteristic classes and calculations in K-theory; modules over the Steenrod algebra and their Ext groups; finite H-spaces and compact Lie groups; maps between classifying spaces of compact groups. Every serious student or practitioner of algebraic topology will want to own a copy of these two volumes both as a historical record and as a source of continued reference. |

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### Contents

Introduction page | xi |

Introduction page | xiii |

Maps between classifying spaces of compact Lie groups | xv |

The cobar construction the Adams spectral sequence higher order | 305 |

On the cobar construction | 27 |

Chern characters revisited and addendum 24 | 29 |

On the structure and applications of the Steenrod algebra | 34 |

Hopf algebras of cooperations for real and complex theory | 36 |

Finite spaces and algebras over the Steenrod algebra and correction | 184 |

On complex Stiefel manifolds | 191 |

On matrices whose real linear combinations are nonsingular | 214 |

On the groups JXI | 222 |

Finite spaces and Lie groups | 235 |

On the groups JX II | 237 |

Spin8 triality F4 and all that | 243 |

The fundamental representations of Es | 254 |

Operations of the nth kind in theory | 60 |

On the nonexistence of elements of Hopf invariant one | 69 |

Stable operations on complex Ktheory | 73 |

Modules over the Steenrod algebra and their Ext groups | 87 |

A periodicity theorem in homological algebra | 93 |

Modules over the Steenrod algebra | 106 |

SubHopfalgebras of the Steenrod algebra | 118 |

What we dont know about RP | 126 |

Calculation of Lins Ext groups | 132 |

The Segal conjecture for elementary abelian groups | 143 |

Applications of Atheory | 154 |

Vector fields on spheres | 161 |

Finite spaces and compact Lie groups | 169 |

spaces with few cells | 178 |

On the groups JXIII | 272 |

On the groups JXIV and correction | 302 |

Atheory and the Hopf invariant | 354 |

Geometric dimension of bundles over RPn | 362 |

2Tori in EK 264 | 367 |

Generalised homology and cohomology theories and a survey | 377 |

Maps between completed classifying spaces | 399 |

Idempotent functors in homotopy theory | 422 |

Uniqueness of BSO | 440 |

Graeme Segals Burnside ring conjecture | 475 |

A generalization of the AtiyahSegal completion theorem | 500 |

Algebraic topology in the last decade | 515 |

### Other editions - View all

The Selected Works of J. Frank Adams: John Frank Adams,J. Peter May,Charles B. Thomas Limited preview - 1992 |

### Common terms and phrases

A-map abelian abelian category acyclic apply associated Atiyah Axiom calculate canonical fibering chain algebra chain complex chain mapping coefficients cohomology operations commutative diagram completes the proof composite consider construct Corollary corresponding cup-product CW-complex define definition degree dimension elements epimorphism equation exact sequence fact factor fibre homotopy filtration finite finitely-generated following diagram formula function functor give graded GROUPS J(X Hirzebruch homological algebra homology homomorphism homotopy equivalence homotopy groups HOPF INVARIANT induced integer isomorphism J. F. ADAMS KA(X KR(X Lemma Massey product Math module monomorphism multiplicative natural subset non-zero notation obtain pair polynomial Proc proof of Lemma proof of Theorem properties Proposition prove Theorem quotient realisation representation result ring satisfy Similarly spectral sequence stable Steenrod algebra Stiefel manifolds subalgebra subgroup sufficient summand Suppose given Theorem 1.1 theory Topology trivial universal example values write zero