By I. M. James (auth.), Gunnar Carlsson, Ralph Cohen, Haynes Miller, Douglas Ravenel (eds.)

These are court cases of a global convention on Algebraic Topology, held 28 July via 1 August, 1986, at Arcata, California. The convention served partially to mark the twenty fifth anniversary of the magazine *Topology* and sixtieth birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and used to be conceived as a successor to the Aarhus meetings of 1978 and 1982. a few thirty papers are incorporated during this quantity, normally at a study point. matters contain cyclic homology, H-spaces, transformation teams, actual and rational homotopy concept, acyclic manifolds, the homotopy idea of classifying areas, instantons and loop areas, and intricate bordism.

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P. 316] remain the is t r i v i a l the W h i t e h e a d S ~ vS 1)-, c = u + d(v), Put us u n d e r s t a n d that a°,c ', write true. nm+l ~ Y" f:-0 for product Recall (p + q - denoted of model ~ p q : S~ + q - 1 to the we m a y veX(Y). *~(a) ~(b) a Whitehead a map corresponding respectively X(X) = x, = y', alterations (~, H,(A(Y),dy), in . 4 of [2] are we may take ± ~ (a) = [~,,~,] = <-~>la'l'lc'lc,a ,. Pq Lemma 5 . 2 . a,,b,,c,, Denote where an e x t e n s i o n whose products. t>2, will ±Wpq:S0P+q-I may be to the AH m o d e l S~ so as with f the recursively put [ao,a 1 ....

The idea of a proof is to verify it for cyclic groups (Theorem 2) and generalized quaternionic groups, and then use a transfer argument to pass from the validity for Sylow subgroups to validity for G. 56 Condition (vii) of Theorem 5 suggests that Conjecture 1 should perhaps be extended to the class of spaces X for which h o m d i m M u . M U . ( X ) < 1. We see no way to attack such a conjecture at the moment. Such a conjecture would be the case n -= 1 of a broader conjecture: There is an isomorphism of graded abelian groups BP.

Whitehead 75(1953), and Serre Proc. and pp. in the 744-752. the Camb. Case Phil. 53-60. "Groupes Whitehead, of d'homotopie Math. et classes 58(1953), pp. tenu & Louvain, groupes 258-294. "The Homology Suspension", Alg@brique, de juin Cotloque de 1956, Masson, 1957. Whitehead, Verlag, P. W. and 2, de facets & s&ries Notes "Loop "On t h e Math. "A C o n n e c t i o n Torsion-Free Paris, of Product", Selick, Soc. 29. C. "Rational pp. Pontrjagin Primes", 698-702. Vol. Quillen, 90(1969), 25. Large without Proceedings Lecture Wilkerson, pp.