Download Algebraic Topology and Transformation Groups: Proceedings of by Stefan Bauer (auth.), Tammo tom Dieck (eds.) PDF

By Stefan Bauer (auth.), Tammo tom Dieck (eds.)

Contents: S. Bauer: The homotopy form 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 different types of genus and degrees above two.- L.G. Lewis, Jr.: The RO(G)-graded equivariant traditional cohomology of advanced 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 resources for Algebraic Topology and Transformation Groups: Proceedings of a Conference held in Göttingen, FRG, August 23–29, 1987

Example text

N=a If a CW complex Y with cells only in even dimensions is regarded as a G-space by assigning it the trivial G-action, then there is an isomorphism of RO(G)-graded Mackey functors ~ ~H*S o ® H * ( Y ; 77) H e* Y = which preserves cup products. For any finite group G, there is a box product operation [] on the category ~Jl of G-Mackey functors which behaves like the tensor product on the category of abelian groups. In particular, ~0l is a symmetric monoidal closed category under the box product.

Following, solu- is as stated: Generator Corollary given in 61 From this theorem we may of course determine any A the linear system II This tion, in this fashion and F c A c F(2) A be any subgroup with is the kernel of a homomorphism Then dim H4(MA) A is a A(G)-equivalent is as stated: to one of the 51 Generators not in Ker(~A) Pl 19 PI' P2 19 PI' q2 16 PI' P2' P3 17 PI' P2' q3 16 PI' P2' ql' q3 17 (Note that here H4(MA) ducible representations of will be a sum of two types of irreG, six cases of this corollary trivial types of irreducibles We mology Dimension of H4(M A) close of by M A.

Unfortunately, this theorem does not apply to complex projective spaces or complex Grassmannians with any reasonable nontrivial G-action because these spaces do not have the right kind of G-CW structure. In fact, if G is ~/p, for any prime p, and r/ is a nontrivial irreducible complex G-representation, then the theorem does not apply to S ~, the onepoint compactification of r1. Moreover, the 2~-graded Bredon cohomology of S n with coefficients in the Burnside ring coefficient system is quite obviously not free over the coefficient system.

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