The Selected Works of J. Frank Adams: Volume 2Cambridge University Press, 7 oct. 1992 - 545 pages J. 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 Few of them have been superseded by later work.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. |
Table des matières
On Chern characters and the structure of the unitary group | 13 |
The Hurewicz homomorphism for MU and BP | 29 |
Operations of the nth kind in Ktheory | 60 |
Stable operations on complex Ktheory | 73 |
Applications of the GrothendieckAtiyahHirzebruch functor KX | 86 |
Modules over the Steenrod algebra and their Ext groups | 87 |
Modules over the Steenrod algebra | 106 |
What we dont know about RP | 126 |
The fundamental representations of Eg | 254 |
On the groups JXIII | 272 |
Maps between classifying spaces of compact Lie groups | 275 |
On the groups JXIV and correction | 302 |
Maps between classifying spaces II | 316 |
Ktheory and the Hopf invariant | 354 |
Geometric dimension of bundles over | 362 |
Generalised homology and cohomology theories and a survey | 377 |
The Segal conjecture for elementary abelian pgroups | 143 |
Finite Hspaces and compact Lie groups | 169 |
Finite Hspaces 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 |
On the groups JXII | 232 |
Finite Hspaces and Lie groups | 235 |
Maps between classifying spaces III | 381 |
Maps between pcompleted 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 |
Two unpublished expository papers | 515 |
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Expressions et termes fréquents
A-module A*-algebra abelian Adams spectral sequence admissible map assume automorphism axioms Classifying Spaces coefficients cohomology commutative completes the proof conjugate consider construct Corollary corresponding CW-complex defined degree dimension dual Dynkin diagram element equivalence exact sequence example Ext groups exterior algebra F₂ filtration FINITE H-SPACES finite number following diagram formula functor G₁ group G H-space homology homomorphism homotopy groups Hopf algebras induced map inductive hypothesis integers irreducible isomorphism J. F. ADAMS K-theory K(BG Lemma Lie group map f Maps Between Classifying Math maximal maximal torus module monomials morphisms non-zero p-complete p-group prime proof of Lemma Proof of Proposition proof of Theorem proves Lemma quotient representation restriction result satisfies SEGAL CONJECTURE spectral sequence spectrum Steenrod algebra Steenrod operations subalgebra subgroup subspace Suppose given Theorem 1.1 theory topology torus unique vector Z₂ zero