Algebraic Topology, Poznan 1989: Proceedings of a Conference by S. Jackowski, B. Oliver, K. Pawaloski

By S. Jackowski, B. Oliver, K. Pawaloski

As a part of the clinical task in reference to the seventieth birthday of the Adam Mickiewicz college in Poznan, a world convention on algebraic topology used to be held. within the ensuing court cases quantity, the emphasis is on immense survey papers, a few awarded on the convention, a few written for that reason.

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The group I~0G(X,p)c has also several natural properties ( cf [10] §6 ). 1 [51] g Xo B ~ and for ~ , 6 > 0 with ~ < fl(~) over f then Remark. Here the go* controlled , f B there is an induced map ~. which makes , X1 K-group a : kGo(X,p), --. functor on such ~Go(X,p)• data. e. there is a map, j , from the constant inverse such that for each to ( f(Go(X,p)e } e > 0 there is a 6 < e and a commutative diagram ~(Go(X,p) c J , (~Go(X,p) , ir, / l ~f(X,p)~ J , ~(X,p)e so that for sufficiently small e the inverse system is constant modulo some relaxation of control Let now X ~ K ~ X be a G-p-t(e)-domination of X by a finite G-complex K .

Soc. 379 (1988). 19. S. Ferry: A slmple-homotopy approach to the finiteness obstruction, Shape Theory and Geometric Topology, pp. 73-81, Lecture Notes in Math. 870, Springer Vlg 1981. 20. M. Gersten: A product formula for Wall's obstruction, Amer. J. Math. 88 (1966), 337-346. 21. K. Iizuka: Finiteness conditions for G-CW-complexes, Japan. J. Math. 10 (1984), 55-69. 22. S. Illman: Smooth equivarlant triangulations of G-manifolds for G a finite group, Math. Ann. 233 (1978), 199-220. 23. S. Illman: The equivarlant triangulation theorem for actions of compact Lie groups, Math Ann.

Ganea in [Ga], which is called the Ganea Hopf Invariant of fi. p o' : Bn ~ B ( G ) classifying ~. c~or is T(*) smashed with the evaluation map eA : EFtEA~ -----4EA,. TS5-Exalnples The following are examples for the application of the theorem mentioned in TS4. Example J, (~P) 44 In the case that B = B , = J , ( E P ) , the n th stage in the James model for QE2P, as defined in CS4, it is shown in [D, II, §4] that there is an element ~1 in the image of J (as defined by Hanks) sudh that all pi-2 o T(wi), for 1 < i < n, can be presented as a sum of elements, each ~f :which is a composition A o #, where p is obtained by smashing ~l with tm identity map of ~he space P 4- P , .

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