Algebraic Topology Homotopy and Group Cohomology: by Alejandro Adem (auth.), Jaume Aguadé, Manuel Castellet,

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

The papers during this assortment, all totally refereed, unique papers, replicate many points of modern major advances in homotopy conception and team 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.- okay. 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 solid splitting: the classifying area of the 4-dim unipotent group.- J.E. McClure, L. Smith: at the homotopy area of expertise of BU(2) on the top 2.- G. Mislin: Cohomologically valuable parts and fusion in groups.

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Extra 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

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22 D e f i n i t i o n . 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 #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.

For m > 1 we denote by p~m the biggest power of p i n m: m = p~"~ + l , 0 < l _< pC'' - 1. 21, for p > 2. P r o p o s i t i o n . A~-module. 1 \ ] Then contoined in M. 1 we need the following lemma. 20). 2 L e m m a . Let M E H then, for any k >_ O, the natural map ~ k ( ~ k M a monomorphism. --* M i~ Proof: The map O k O ~ k M -~ M is the composition ~ k O ~ k M ~ O k ~ k M ~ M where the first map is induced by the inclusion ( ~ k M ~ (~kM and the second is the natural map. It suffices to prove the lemma for k = 1 (k = 0 is trivial).

PESCItKE and M. PFENNIGER, On orthogonal pairs in categories and localization, preprint (1990). [14] P. HALL, Some constructions for locally finite groups, J. London Math. Soc. 34 (1959), 305-319. [15] P. HILTON, On the extended genus, Acta Math. Sinica (N. ) 4 (1988), no. 4, 372-382. [16] P. HILTON, G. MISLIN and J. ROITBERG, Localization of N{lpotent Groups and Spaces, North-Holland Math. Studies 15 (1975). [17] R. C. LYNDON and P. E. ScItuPP, Combinatorial Group Theory, Ergeb. Math. Grenzgeb.

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