By Nigel Ray, Grant Walker

J. Frank Adams had a profound effect on algebraic topology, and his works proceed to form its improvement. The overseas Symposium on Algebraic Topology held in Manchester in the course of July 1990 used to be devoted to his reminiscence, and nearly all the world's prime specialists took half. This two-volume paintings constitutes the court cases of the symposium. The articles contained right here variety from overviews to stories of labor nonetheless in development, in addition to a survey and entire bibliography of Adams' personal paintings. those lawsuits shape a big compendium of present examine in algebraic topology, and one who demonstrates the intensity of Adams' many contributions to the topic. the following within the first quantity the topic is especially volatile homotopy thought, homological and express algebra. the second one quantity is orientated towards sturdy homotopy idea, the Steenrod algebra and the Adams spectral series.

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**Extra resources for Adams Memorial Symposium on Algebraic Topology: Volume 1**

**Example text**

The ultimate goal of Section 3 is to construct a free model for a twisted tensor productof two DGA's. f B Op,, CSZF. We will therefore have a weak equivalence between the Adams-Hilton model for E and the free model of a twisted tensor productof the Adams-Hilton models for B and F. With motivation from Tanre's twisted product of differential graded Lie algebras, we now make the following Definition. ) The sequence 0 -* (B,e)(A®B,D)7r , (A, d) -> 0 is a sequence of DGA morphisms, exact at (A, d) and (B, e), where t(b) = 10 b and ir(a 0 b) = e(b)a.

France 87 (1959), 277-280. 13. Expose sur les travaux de C. T. C. Wall sur l'algebre de cobordisme Il, Bull. Soc. Math. France 87 (1959), 281-284. 14. On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960), 20-104. 15. Appendix to a paper of E. R. Reifenberg, Acta Math. 104 (1960), 76-91. Bibliography of J. F. Adams 23 16. The sphere, considered as an H-space mod p, Quart. J. Math. Oxford Ser. (2), 12 (1961), 52-60. 17. A finiteness theorem in homological algebra, Proc.

P-adic completions in equivariant cohomology. Topology 26(1987), 413-433. 18 May: The work of J. F. Adams in the homotopy category of connected CW-complexes which ensure, by Brown's theorem, that S is the set of equivalences for an idempotent functor. The key axiom, which is hard to verify in practice, is an analog of the solution set condition in the adjoint funetor theorem. In fact, this paper results from a failed swindle presented in 1973 lectures at Chicago. Adams presented the theory without the solution set analog, thereby constructing localizations and completions without doing a shred of work.