By Nigel Ray, Grant Walker
J. Frank Adams had a profound impression 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 was once devoted to his reminiscence, and nearly the entire world's best specialists took half. This two-volume paintings constitutes the lawsuits of the symposium. The articles contained the following variety from overviews to studies of labor nonetheless in growth, in addition to a survey and whole bibliography of Adams' personal paintings. those complaints shape a massive 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 subject is especially volatile homotopy idea, homological and express algebra. the second one quantity is orientated towards sturdy homotopy conception, the Steenrod algebra and the Adams spectral series.
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This article suits any direction with the note "Manifold" within the identify. it's a graduate point publication.
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Press 1974, 1-9. Bibliography of J. F. Adams 25 49. Stable Homotopy and Generalised Homology, Univ. of Chicago Press 1974. 50. Sub-Hopf-algebras of the Steenrod algebra, Proc. Cambridge Philos. Soc. 76 (1974), 45-52. 51. Geometric dimension of bundles over RP", Publ. Res. Inst. Math. , Kyoto Univ. (1974), 1-17. 52. Idempotent functors in homotopy theory, in Manifolds - Tokyo 1973, Univ. of Tokyo Press 1975, 247-253. 53. (with A. Liulevicius) Buhstaber's work on two-valued formal groups, Topology 14 (1975), 291-296.
P. May (with contributions by Nigel Ray, Frank Quinn, and J. Tornehave) E,o ring spaces and E,o ring spectra. Springer Lecture Notes in Mathematics Vol 577, 1977]. May: The work of J. F. (SO) -4 7rr. Here d = 0 except in the real case with r - 1 or 2 mod 8, when d detects a direct summand Z2 V- Im J generated by elements µ,. For any r, the real e invariant detects Im J as a direct summand, the case r - 7 mod 8 being incomplete in the paper since the full Adams conjecture was not yet available. Various composition products and Toda brackets are detected by means of Yoneda and Massey products in the target groups.
He conExtA(E-1Z2, Z2), and he explains how this jectures that ExtA(P, Z2) might come about in terms of the sub Hopf algebras A,.. Calculation of Lin's Ext groups (1979, with W. H. Lin, Don Davis, and Mark Mahowald)  This paper gives Adams' simplification of Davis and Mahowald's simpli- 6. fication of Lin's proof of Adams' Ext conjecture just stated. Exactly as Adams envisioned, the proof is by inductive use of the Ar. This implies the Segal conjecture for Z2, although the topology is not presented here.