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 used to be devoted to his reminiscence, and nearly the entire world's top specialists took half. This two-volume paintings constitutes the court cases 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 complaints shape a big compendium of present study in algebraic topology, and person who demonstrates the intensity of Adams' many contributions to the topic. right here within the first quantity the subject matter is especially volatile homotopy thought, homological and express algebra. the second one quantity is orientated towards strong homotopy idea, the Steenrod algebra and the Adams spectral series.
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Additional info for Adams Memorial Symposium on Algebraic Topology: Volume 1
F. Atiyah) K-theory and the Hopf invariant, Quart. J. Math. Oxford Ser. (2) 17 (1966), 31-38. 35. On the groups J(X)-IV, Topology 5 (1966), 21-71; with a correction, ibid. 7 (1968), 331. 36. A periodicity theorem in homological algebra, Proc. Cambridge Philos. Soc. 62 (1966), 365-377. 37. A survey of homotopy theory, Proc. Internat. Congr. Math. 1966, MIR, Moscow 1968, 33-43. 38. Lectures on Lie groups, W. A. , New York 1969. (Reprinted by Univ. ) 39. Lectures on generalised cohomology, in Category Theory, Homology Theory and their Applications III, Lecture Notes in Math.
Let a : R(G) -> K(BG) be the natural map. With X = BG, Im(a) C FF(BG). Adams proves that equality holds if G is finite or if iro(G) is the union of its Sylow subgroups. In these cases, f* : K(BG') -. K(BG) carries R(G') into R(G) for any map f : BG -+ BG', but this is not true in general. However, for any G there is an n > 0 such that nFF(BG) C Im(a). If G is monogenic and x E FF(BG), then x = a(p) for an honest representation p of G, but there is a finite p-group G and an element x E FF(BG) such that x is not of the form a(p) for any representation p.
Bourbaki 1984-85, No. 645, Asterisque 133-134 (1986), 255-260. 75. Maxwell Herman Alexander Newman, Biographical Memoirs of Fellows of the Royal Society 31 (1985), 437-452. 76. (with J. H. Gunawardena and H. Miller) The Segal conjecture for elementary abelian p-groups, Topology 24 (1985), 435-460. 77. 2-Tori in E8, Math. Ann. 278 (1987), 29-39. 78. -P. Haeberly, S. Jackowski and J. P. May) A generalisation of the Segal conjecture, Topology 27 (1988), 7-21. 79. -P. Haeberly, S. Jackowski and J. P.
Adams Memorial Symposium on Algebraic Topology: Volume 1 by Nigel Ray, Grant Walker