Adams Memorial Symposium on Algebraic Topology: Volume 1 by Nigel Ray, Grant Walker

By Nigel Ray, Grant Walker

J. Frank Adams had a profound impact 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 nearly the entire world's best specialists took half. This two-volume paintings constitutes the lawsuits of the symposium. The articles contained right here diversity from overviews to experiences of labor nonetheless in development, in addition to a survey and entire bibliography of Adams' personal paintings. those court cases 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 principally risky homotopy concept, homological and specific algebra. the second one quantity is orientated towards reliable homotopy idea, the Steenrod algebra and the Adams spectral series.

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He was especially generous and helpful to young mathematicians just starting out. There are many proofs attributed to Adams in the work of others, and there are many proofs and some essentially complete rewrites that come from his "anonymous" referee's reports. He wrote many perspicacious comments on papers for Mathematical Reviews. He was a force to be reckoned with at any occasion such at this, and his guiding presence and astute questions enlivened many a conference. As the two unpublished papers illustrate, Frank throughout his career made it his business to learn and assimilate fully all of the most important new developments in algebraic topology.

Dj(h®m) = bh®m+(-1)degh(h®em+E= denotes the action of A on M. ® hi" and 0(h) = E j h; A straightforward calculation shows that D' = 0 and eDqS = 0. X, which will denote the non-degenerate singular cubical chains on a topological space X. For any n > 0 and (n - 1)-connected pointed topological space X, C. X of simplices sending the (n - 1)-skeleton of cubes to the basepoint of X. X is presented in [Al; Sec. 7]. Note that since we are using cubical instead of singular chains, the usual "front p-face tensor back (n - p)-face" Alexander-Whitney diagonal does not work.

For any f : BG -* BG', f* : K(BG') --+ K(BG) carries R(G') into R(G). There is a detailed Lie theoretic analysis of admissible maps, and there are lots of concrete calculational examples and case by case calculations. This paper initiated serious work on this topic, long before others were interested. The talks of Jackowski, Stewart Priddy, and others made clear that this is now a thriving area of algebraic topology. 2. Maps between classifying spaces II (1978) [62] In this fascinating and relatively neglected paper, G and G' are compact, but not necessarily connected, Lie groups.

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