By Alejandro Adem (auth.), Jaume Aguadé, Manuel Castellet, Frederick Ronald Cohen (eds.)

The papers during this assortment, all totally refereed, unique papers, mirror many elements of contemporary major advances in homotopy thought and workforce cohomology. From the Contents: A. Adem: at the geometry and cohomology of finite basic groups.- D.J. Benson: Resolutions and Poincar duality for finite groups.- C. Broto and S. Zarati: On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C. Ravenel: Morava K-theories of classifying areas and generalized characters for finite groups.- ok. Ishiguro: Classifying areas of compact uncomplicated lie teams and p-tori.- A.T. Lundell: Concise tables of James numbers and a few homotopyof classical Lie teams and linked homogeneous spaces.- J.R. Martino: Anexample of a strong splitting: the classifying house of the 4-dim unipotent group.- J.E. McClure, L. Smith: at the homotopy strong point of BU(2) on the best 2.- G. Mislin: Cohomologically significant parts and fusion in groups.

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Additional info for Algebraic Topology Homotopy and Group Cohomology: Proceedings of the 1990 Barcelona Conference on Algebraic Topology, held in S. Feliu de Guíxols, Spain, June 6–12, 1990

Example text

2. Now assume given a prime p and an idempotent functor Ep as in (c). 3, the standard map p~ : S 1 --* S 1 of degree n is an Ev-equivalence if (n,p) = 1, and thus, for every space X, the map (pn)*: IS ~, EpX] ~ [S 1, EpX] is a bijection. This tells us that ~r~(EpX) is a p-local group and hence separable. If we assume that (b) holds, then in particular ~: X ---* EvX is nuUhomotopic, and the universal property of 77forces EpX to be contractible. This shows that ( b ) ~ ( c ) . The implication ( c ) ~ ( d ) is trivial.

This situation is typical as shown by the main result in [2]. 34 References 1. I. BOKOR, On Genus and Cancellation in Homotopy, Israel Journal of Mathematics 2. I. LLERENA,Wedge Cancellation of Certain Mapping Cones, Composi$io Mathe- (in press). matica (to appear). I. Bokor: Mathematik Berninaplatz 3 CH-8057 - Zfirieh Switzerland I. Llerena: Departament d'Algebra i Geometria Universitat de Barcelona Gran Via de les Corts Catalanes, 585 E-08007 Barcelona Spain 1990 Barcelona Conference on Algebraic Topology.

Durham Symposium on Homotopy Theory 1985, (1987), 97-116. [LS] J. LANNES AND L. SCIIWARTZ, Sur la structure des A~-modules instables injectifs, Topology 28 (1989), 153-169. [LZ1] J. LANNES AND S. ZARATI, Sur les L/-injectifs, Ann. Scient. Ec. Norm. Sup. 19 (1986), 303-333. [LZ2] 25-59. , Foncteurs d~riv~s de la d@stabilisation, Math. Z. R. MILLER, The Sullivan conjecture on maps from classifying spaces, Annal~ of Math 120 (1984), 39-87. IS] L. SCHWARTZ, La filtration nilpotente de la cat@gorie L¢ et la cohomologie des espaces de lacets, in "Algebraic Topology Rational Homotopy, Louvain 1986," Lecture Notes in Math 1318, Springer, 1988.

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