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 global convention on algebraic topology used to be held. within the ensuing lawsuits quantity, the emphasis is on gigantic survey papers, a few awarded on the convention, a few written to that end.
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Additional resources for Algebraic Topology, Poznan 1989: Proceedings of a Conference Held in Poznan, Poland, June 22-27, 1989
6 C(X(t))I~°(z[%(wH)*]) c(x) --* @ fA(x) The equivarlant finiteness obstruction ~G(X) @ N I(o(Z[~0(WH)*]). decomposes into the family of obstructions wH~(x) . Precisely, the image of the (H/Q-component ~G(X)~ of the obstruction #G(X) under epimorphlsm Wh(,o(WH)*x is equal to the equivariant Wall-type obstruction z) --. ]) wHa(x) . The proof of this result is technical in nature and we refer for it to , 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.
L ( p , pa ), where l(p, Pl ) is the double mapping cylinder of p and Pl, mad p is the obvious map between the double mapping cylinders. The theorem of Held and Sjerve is obtained as the particular case when both A and E1 equal a point. Then ** is a presentation of M as a nmpping cone M = B Ug CC, and * says that there exists a ill)ration p : E ~ B which restricts to a fibration PB : EB ----* B. f "*:PA)specializes to be C * F. 3 presents T(kI) as a mapping cone T(B) Uw C(C * F). Iterated usage of ** gives the result stated in CS6.
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. Math. Helv. 51 (1976), 611626. 44. F. Quinn: Ends of maps, II, Invent.