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

ISBN-10: 0387551956

ISBN-13: 9780387551951

The papers during this assortment, all absolutely refereed, unique papers, mirror many facets of contemporary major advances in homotopy concept and staff 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 easy 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 good splitting: the classifying house of the 4-dim unipotent group.- J.E. McClure, L. Smith: at the homotopy forte of BU(2) at the leading 2.- G. Mislin: Cohomologically principal parts and fusion in teams.

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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 Guixols, **

**Sample text**

But we also have the equality so that d =- kg (mod m). Since by choice I < k < m - 1, either g # +1 - - in which case A is not a homotopy equivalence - - or d # =t=1--. in which case det(A(~)) = ad # 4-1 and is not a homotopy equivalence. Hence Cfl and Cg1 cannot be homotopy equivalent, completing the verification of (iv). Note, however, that CI1 and Cg1 are in fact of the same genus. To verify this, it is only necessary to localise at the primes dividing m, the order of y. But choosing a -- 1, b = 0, d = k in ~ and A = ids4,-1 above defines an equivalence at each such prime, since k is coprime to m.

BERRICK, Two functors from abelian groups to perfect groups, J. Pure Appl. Algebra 44 (1987), 35-43. [5] A. J. BERRICK, Universal groups, binate groups and acyclicity, in: Group Theory, Proceedings of the 1987 Singapore Conference, Walter de Gruyter, Berlin-New York, 1989, 253-266. [6] A. J. BERRICK, Torsion generators for all abelian groups, J. Algebra, to appear. [7] A. J. BERRICK and C. F. MILLER III, Strongly torsion generated groups, preprint (1990). [8] A. K. BOUSFIELD, The localization of spaces with respect to homology, Topology 14 (1975), 133-150: [9] C.

A ( : ) ' ) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = H(gl V g~)(A(~) O h ) = H((gl v g~) o ¢) and Z(~ o (fl V f2)) = A(~)Z(fl V f2) 1 0 0 0 0 ky vy 0 0 k v 0 0 m u 0 0 0 0 1 0 0 0 0 0 0 0 uky 0 whereas Hence E(~o(fl V f2)) -~ E((gl Vg2)o¢) since u k - 1 (mod m), showing that CI1 VCi2 and Cg, V Cg2are homotopy equivalent, thereby completing the verification of (i). 00lLet ~ be the self homotopy equivalence of S 2n V $2" given by Then 33 since m is the order of y. Thus ~ and the identity map o n S 4n-1 induce a homotopy equivalence between CI2 and Cg2.

### Algebraic Topology: Homotopy and Group Cohomology : Proceedings of the 1990 Barcelona Conference on Algebraic Topology, Held in S. Feliu De Guixols, by Barcelona Conference on Algebraic Topology 1990 San Feliu De Guixols, Manuel Castellet, J. Aguade, Frederick R. Cohen

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