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 global convention on algebraic topology was once held. within the ensuing complaints quantity, the emphasis is on enormous survey papers, a few offered 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 obstruction vanishes in the case that the base of ~ is a double suspension. In all the classical cases, ~he base is a highly connected sphere and the obstruction vanishes: T S 3 - T h e structure of T2 43 Given a presentation B = B2 = ((* U C A o ) U CA1 ), the following presentation is obtained: T = T2 = ((T(*) U C(Ao A T(*))) U C(A1 AT(*))), with attaching maps T ( f l ) mid T(f2). Thus, as T ( f l ) is known, only T(f~) is needed in order to give a full description of T2. The main theorem of [Hal], was shown in [D, I, §6], to describe the homotopy class of the relative attaching map Po o T(f2), (in the case that A1 is a suspension) which is an element in the set [A1 AT(*}, EA0 AT(*}].

1 ). We also need the notion of so-called equivariant Euler characteristic which is the UFAI for the category of finite G-complexes. First we define a functor A G : G-Top ---+ Ab. For G-space X we put AG(X) to be the free abelian group generated by the set CI(X). A G-map f : X ---* Y induces a homomorphism AG(f):AG(X) --. A G ( y ) . Let X be a G-space that is finitely G-dominated. o(WH)*]) cI(x) and wa(X) = ~ w~(X) . 3 (a) The pair (AG,x G) is the UFAI for the category of G-spaces having the G-homotopy type of a finite G-complex.

S. Kwasik: On equivariant finiteness, Compositio Math. 48 (1983), 363-372. 32. S. Kwasik: Locally smooth G-manifolds, Amer. 3. Math. 108 (1986), 27-37. 33. W. Liick: The geometric finiteness obstruction, Proc. London Math. Soc. 54 (1987), 367-384 34. W. Lfick: Transformation groups and algebraic K-theory, Lecture Notes in Math. 1408, Springer Vlg 1989. 35. I. B. C. Wall: The topological spherical space form problem-II; existence of free actions, Topology 15 (1976), 375-382. 36. I. Madsen, M. Rothenberg: On the classification of G-spheres Ilh TOP automorphism groups, preprint 14 (1985), Aarhus Univ.

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