By Stefan Bauer (auth.), Tammo tom Dieck (eds.)
Contents: S. Bauer: The homotopy kind of a 4-manifold with finite primary group.- C.-F. Bödigheimer, F.R. Cohen: Rational cohomology of configuration areas of surfaces.- G. Dylawerski: An S1 -degree and S1 -maps among illustration spheres.- R. Lee, S.H. Weintraub: On convinced Siegel modular forms of genus and degrees above two.- L.G. Lewis, Jr.: The RO(G)-graded equivariant traditional cohomology of complicated projective areas with linear /p actions.- W. Lück: The equivariant degree.- W. Lück, A. Ranicki: surgical procedure transfer.- R.J. Milgram: a few comments at the Kirby - Siebenmann class.- D. Notbohm: The fixed-point conjecture for p-toral groups.- V. Puppe: easily hooked up manifolds with no S1-symmetry.- P. Vogel: 2 x 2 - matrices and alertness to hyperlink idea.
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Additional info for Algebraic Topology and Transformation Groups: Proceedings of a Conference held in Göttingen, FRG, August 23–29, 1987
GX are projective over H ~ S ° 64 when X is constructed from a slightly more general class of even-dimensional cells. Since 72/2 has only one nontrivial irreducible representation, I t e* S easy to describe when G = 7//2. 1. If G = 22/2 and s E RO(G), then if lal = Is el = o, if Isl = 0, [ s e l < 0, and let el is even, if tetl = 0, t a e i _< 1, and t a e i i s o d d , if letl = 0, Is el > o, and let Gi is even, if IetI = 0, let et > 1, and let el is odd, if Isl # 0 arid let eI = 0, if letl > 0, I s e l < 0, and ietel is even, if letl < 0, Io, el > 1, and letel is odd, otherwise.
The counterexamples have some interesting connections with the equivariant Hurewicz theorem [LE1]. All of these topics are being investigated. All of the results in this paper depend on the observation that equivariant cohomology theories are Mackey functor-valued. Therefore, the first section of this paper contains a discussion of Mackey Mnctors for the group 7//p. In the second section, we discuss the RO(G)-graded cohomology of a point, precisely define what we mean by a G-CW complex, and prove our "freeness" theorem.
F) If M is a Mackey functor, then L(M(e) p) ~ R(M(e) p) is denoted M G. There are two reasonable choices of a G action on M(e) p, the permutation action or the composite of the permutation action and the given action of G on each factor M(e). These actions yield isomorphic g[G]-modules, so the choice is not important. The simple permutation action is always assumed here. The assignment of M G to M is a special case of an important construction in induction theory [DRE, LE2] that assigns a Mackey functor M b to each object b of B(G) and each Mackey functor M.
Algebraic Topology and Transformation Groups: Proceedings of a Conference held in Göttingen, FRG, August 23–29, 1987 by Stefan Bauer (auth.), Tammo tom Dieck (eds.)