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 job in reference to the seventieth birthday of the Adam Mickiewicz collage in Poznan, a world convention on algebraic topology used to be held. within the ensuing lawsuits quantity, the emphasis is on large survey papers, a few awarded on the convention, a few written subsequently.

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Extra resources for Algebraic Topology Poznań 1989: Proceedings of a Conference held in Poznań, Poland, June 22–27, 1989

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F, a(,f) : A ----* f t ~ X , composing it with the k th combinatorial extension nmp, giving the composition A ~ f~EX ~ flEX ^" and then adjointing back again giving H k ( f ) : E A E X ^~. Thus not only that James' H2 extends Whiteheads' definition (up to sign) of the operator H h)r any dimension q mxd fox' every space X (giving Whiteheads ~ case as a sphere), also the other H~, called nowadays the higher James Hapf Invarianta were introduced by Janms. Thus there are many Hopf Invmlants indexed by N, and using them it is clear that tim E H P sequence stops being exact exactly when H~ becomes non zero.

197. The controlled equivariant boundary theorem is closely related to:the equivariant product structure theorem. Namely, let a G-manifold M be provided with a locally smooth PL structure ~0 consider locally smooth PL structures ~ near aM . We on M x R which agree with ~0 x R near aM x R (so-called structures rel 8). We say that a structure 5] on M x R tel a admits a product structure if 5] is G-isotopic rel a to a structure of the form e x R , where e is a locally smooth PL structure on M which agrees with ~'0 near a M .

Suppose F is a simply connected r-dimensional integral homology rsphere. Then there exists a finite G-complex X homotopy equivalent to Sr÷dn. Moreover G acts semifreely on X with X G = F. g. [9], [59] ~2). It turns out that - at least under some restrictions - the equivariant finiteness obstruction is closely connected with the problem of existence of regular neighbourhoods. This observation was made by F. Quinn [44] prop. 2 and cot. 3 and K. H. Dovermann [16]. For instance, if a finite group G acts locally smoothly and semifrecly on a compact manifold neighbourhood in M M then the fixed point set M G has an equivariant closed regular iff all equivariant finiteness obstructions wH(M)'s vanish.

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