Algebraic Topology Poznań 1989: Proceedings of a Conference by C. Allday, V. Puppe (auth.), Stefan Jackowski, Bob Oliver,

By C. Allday, V. Puppe (auth.), Stefan Jackowski, Bob Oliver, Krzystof Pawałowski (eds.)

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 complaints quantity, the emphasis is on immense survey papers, a few awarded on the convention, a few written subsequently.

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X. S/¢I where the generator r in the free lie algebra has coordinates {kl, k2 . . . kt}, the nmp Hr : S q -----*~Xr is a generalization of the Hopf Invariant, and the map w~ : ~ X r ~ S p V S t' is a. successive composition of whitehead product maps. H I 4 - T h e work o f J . Hilton were generalized by that of Milnor [Mil]. He was able to produce all the results obtained by Hilton (and mentioned in HI3) to the case when S q is replaced by a space E P and S p is replaced by a space EA. f is an infinite sum as before, indexed by r in the Hall basis of a free Lie algebra on two variables.

36 18. H. Dovermann, M. Rothenberg: Equivariant surgery and classification of finite group actions on manifolds, Memoirs Amer. Math. 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.

It is natural to ask whether the equivariant finiteness obstruction can be applied to produce an equivariant boundary in a smooth open G-manifold. fy all details. Up to the author's knowledge nobody has presented the equivariant version of Siebenmann's theorem in final written form and we only outline some constructions in the ease of a smooth G-manifold. 30 The existence of the G-collar neighbourhood of the boundary reduces the question to the following : when does a G-end g of a smooth open G-manifold M admit an equivariant collar neighbourhood ?

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