By Barcelona Conference on Algebraic Topology 1990 San Feliu De Guixols, Manuel Castellet, J. Aguade, Frederick R. Cohen

The papers during this assortment, all absolutely refereed, unique papers, mirror many points of modern major advances in homotopy concept and crew cohomology. From the Contents: A. Adem: at the geometry and cohomology of finite uncomplicated 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.- okay. Ishiguro: Classifying areas of compact basic 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 sturdy splitting: the classifying area of the 4-dim unipotent group.- J.E. McClure, L. Smith: at the homotopy distinctiveness of BU(2) at the best 2.- G. Mislin: Cohomologically principal parts and fusion in teams.

**Read Online or Download Algebraic Topology: Homotopy and Group Cohomology : Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Held in S. Feliu De Guixols, PDF**

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**Sample text**

If a group G is not separable, then one cannot expect to recover full information about G from the family of its p-localizations Gp. The worst possible situation occurs, of course, when all these vanish. We introduce new terminology to analyze this case. 2 A group G is called generically trivial if Gp = 1 for all primes p. As next shown, it turns out that such groups cannot be detected by any idempotent functor extending p-localization of nilpotent groups to all groups. The basic facts about idempotent functors and localization in arbitrary categories are explained in [1,13].

GSZ] P. GOERSS, L. SMITII AND S. ZARATI, Sur les A~-alg~bres instables, in "Algebraic Topology, Barcelona 1986," Lecture Notes in Math. vol. 1298, Springer, 1987. W. HENN, Some finiteness results in the category of unstable modules over the Steenrod algebra and application to stable splittings; Preprint. W. HENN, J. LANNES AND L. SCItWARTZ,The categories of unstable modules and unstable algebras modulo nilpotent objects; Preprint. , Nil-localization of cohomology of BG; In preparation. M. KANE, "The homology of Hopf Spaces," North Holland Math.

An object K of K is called m-nilpotent (resp. m-reduced, 22ilr,closed) if the underlying unstable A~-module is m-nilpotent (resp. m-reduced, Nil,n- closed) Assume that M and N are objects of/if, #r: M --~ 22~-1(M) the 22ilr-localization of M and/~8: N -* 22~-1(N) the 22ils-localization of N. Then the diagram M ®N M ® 2221(M) #r®l ~r®l ~ 22~-a(M) ® N 11®.. -isomorphism vertical arrows and Hil~-isomorphism horizontal arrows. Af~-~(M)®2q'~-:(N) is A/'ilm~,(~,~)-isomorphism. (~e)-isomorphisms. 23 Proposition.