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 was once held. within the ensuing complaints quantity, the emphasis is on big survey papers, a few provided on the convention, a few written subsequently.

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38. R. Oliver: Fixed-point sets of group actions on finite acycllc complexes, Comment. Math. I-Ielv. 50 (1975), 155-177. 39. R. Oliver: Smooth compact Lie group actions on disks, Math. Zeit. 149 (1976), 79-96. 40. R. Oliver: G-actions on disks and permutation representations II, Math. Zeit. 157 (1977)~ 237-263. 41. R. Oliver: G-actlons on disks and permutation representations, 3. Algebra 50 (1978), 4462. 42. R. Oliver, T. Petrie: G-CW-surgery and Ko(ZG), Math. Zeit. 179 (1982), 11-42. 43. T. Petrie: G-maps and the projective class group, Comment.

There is an equivariant handle decomposition of M on a closed collar of N iff the cur,trolled equivariant finiteness obstruction Crc(M,N) is zero in KGo(M)c . The idea of the proof is to adapt the Kirby-Siebenmann argument [28], Essay III to the equivariant, locally smooth context by means of the equivariant product structure theorem above. There is also an isovariant velsion without "gap hypothesis" [47] thm 8. We have already mentioned that (generally) the control-relaxation map is not injective.

The proof of this result is technical in nature and we refer for it to [2], thm. 1. In order to relate Liick's obstruction wG(X) to wHa(X)'s a sort of the realization result for the equivariant finiteness obstruction is needed. _~7 let Y be a finite G-complex and let { w~ } , wH~ E [ ( o ( I [ % ( W H ( Y ) ) ~ ] ) denote an arbitrary family of elements. (wH(X)) = ~ . 3. It also goes by induction on the number of elements of the set CI(Y) and the inductive step is based on the analogous realization result for relatively free action.

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