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 global convention on algebraic topology was once held. within the ensuing court cases quantity, the emphasis is on sizeable survey papers, a few provided 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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This theorem follows from the work of Held and Sjerve [HS], which followed that of Wall tWill(mentioned in TS6 below). In §3 they prove that given a cofiber sequence A ~ f X ~ C f, and a. 4]. f o i)*(~) over A. 5], states that in the particular case that X is a point and C I is homotopic to ZA, (A * Y) g-~ ~I" is homotopic to the Hopf construction of the clutching nmp A x ]" ---* A after both maps are suspended once. 17]. B the base of ( has a conic presentation B0 C B1 C ... ((* U CA1) U C(A2)) tO ...

It is well-known that any compact G-ANR is finitely G-dominated ( see [37] prop. 1 or [30] ). In particular, it applies to G-manifolds. If M is a compact manifold with smooth G-action then the triangulation results of S. Illman [22], [23] show that M carries the structure of a finite G-complex. If we assume that the action of the group G is locally smooth then the situation changes drastically. othenberg [18] §12 and Weinberger [60] p. 532 or [61] thm 16(a) show that the equivariant finiteness obstruction of M can be non-zero for certain M and a suitable finite 29 group G .

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. 262 (1983), 487-501. 24. S. Illman: A product formula for equivariant Whitehead torsion and geometric applications, Transformation Groups, Pozna~. 1985, pp. 123-142, Lecture Notes in Math. 1217, Springer Vlg 1986.

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