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 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 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 reliable splitting: the classifying house of the 4-dim unipotent group.- J.E. McClure, L. Smith: at the homotopy forte of BU(2) at the top 2.- G. Mislin: Cohomologically primary parts and fusion in teams.

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1990 Barcelona Conference on Algebraic Topology. T H E C L A S S I F I C A T I O N OF 3 - M A N I F O L D S W I T H S P I N E S R E L A T E D T O F I B O N A C C I G R O U P S (*) ALBERTO CAVICCHIOLI AND FULVIA SPAGGIARI Abstract We study the topological structure of closed connected orientable 3-manifolds which admit spines corresponding to the standard presentation of Fibonacci groups. 1. Introduction. A spine of a closed 3-manifold M is a 2-dimensional subpolyhedron such that M \ (open 3-cell ) collapses onto it.

In general, a perfect group need not be generically trivial. 1] and hence separable [22, ยง9]. Further, in Section 4 below, we present an example of a countable perfect group whose localizations contain the localizations of all finitely generated nilpotent groups. However, as next shown, finite perfect groups are generically trivial. 6 For a finite group G, the following assertions are equivalent: (a) G is generically triviab (b) G is perfect; (c) for every prime p, G is generated by p'-torsion elements.

It is proved in [LS] that N is nilpotent if and only if for any x E N, there exists r > 0 such that Sq~x = 0 (Sqo r times). 9 is now equivalent to the following statement. An unstable A~-module is m-nilpotent if and only if for any x E N and for any k: 0 < k < m, there exists rk >_ 0 such that Sq~k*x = 0 (Sqk rk-times) (see iS]). Characterization o f m - r e d u c e d u n s t a b l e A ~ - m o d u l e s . 11 P r o p o s i t i o n . Let M be an unstable A~-module. The following are equivalent. (1) M is m-reduced.