By Nigel Ray, Grant Walker

J. Frank Adams had a profound effect on algebraic topology, and his works proceed to form its improvement. The foreign Symposium on Algebraic Topology held in Manchester in the course of July 1990 was once devoted to his reminiscence, and almost all the world's major specialists took half. This two-volume paintings constitutes the complaints of the symposium. The articles contained the following variety from overviews to reviews of labor nonetheless in development, in addition to a survey and entire bibliography of Adams' personal paintings. those lawsuits shape an enormous compendium of present examine in algebraic topology, and person who demonstrates the intensity of Adams' many contributions to the topic. right here within the first quantity the topic is principally risky homotopy concept, 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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Finally, an approximation of X in the form X W A M, where W has finite skeleta and M is the Moone spectrum for Z(p) or Z(p), gets around the convergence problem for the ASS. As important motivating examples, it follows that BSO® and, when p > 2, F/PL are equivalent to BSO as infinite loop spaces. Stewart Priddy told us something about his collaboration with Frank on this project. Actually, I proposed the problem to both authors, but my own May: The work of J. F. Adams 19 ideas on the subject led nowhere.

Moreover, any 14 May: The work of J. F. Adams -9 is induced by a map f defined after finite localization. Conversely, given an admissible map cp, there is a unique homomorphism t9 such that the diagram commutes, and z9 can be induced by a map f defined after finite localization. Thus there is a bijective correspondence between homomorphisms t9 induced by maps f defined after finite localization and W'-equivalence classes of admissible maps cp. For any f : BG -* BG', f* : K(BG') --+ K(BG) carries R(G') into R(G).

Finite H-spaces and Lie groups, J. Pure Appl. Algebra 19 (1980), 1-8. 67. Spin(8), triality, F4 and all that, in Superspace and Supergravity, ed. S. W. Hawking and M. Rocek, Cambridge Univ. Press 1981, 435-445. 68. Graeme Segal's Burnside ring conjecture, Bull. Amer. Math. Soc. (NS) 6 (1982), 201-210. (Also in Proc. Symp. Pure Math. 39, Part 1, Amer. Math. Soc. ) 69. Graeme Segal's Burnside ring conjecture, Contemp. Math. 12, Amer. Math. Soc. 1982, 9-18. 70. Maps from a surface to the projective plane, Bull.