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

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 yes Siegel modular different types of genus and degrees above two.- L.G. Lewis, Jr.: The RO(G)-graded equivariant usual 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 concept.

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Extra info for Algebraic Topology and Transformation Groups: Proceedings of a Conference held in Göttingen, FRG, August 23–29, 1987

Example text

If G = 27/p, then the box product M [] N of Mackey functors M and N is described by the diagram I-M(1) ® N(1) ® M(e) ® N ( e ) ] / ~ M(e) ® N(e) 0 The equivalence relation ~ is given by x®ry ~ px®y for x C M(1) and y e N(e) rv®w ,,~ v®pw for v C M ( e ) a n d w C N(1). The action 0 of G on M(e) @ N(e) is just the tensor M(e) and N(e). The map r is derived from the summand of the direct sum used to define M rlN(1). on the first summand and the trace map of the action product of the actions of G on inclusion of M ( e ) ® N(e) as a The map p is induced by p ® p 0 on the second.

A module over S is just a Mackey functor M together with an action map ~:SDM--* M making the appropriate diagrams commute. Since the Burnside ring Mackey functor A is the unit for [], it is a Mackey functor ring whose multiplication is the isomorphism A []A ~ A and whose unit is 63 the identity m a p A --* A. Every Mackey functor is a module over A with action m a p the isomorphism A [ ] M -~ M. 1(h) is a Mackey functor ring. Similar remarks apply in the graded case. ~ for ~ and /3 in RO(G). The following result characterizes maps out of box products and allows us to describe a Mackey functor ring S in terms of S(1) and S(e).

The group loops around denote them around ~ of the 0 and by cover (Z/2) I in the base, p and is then 2 r = pq, + (Z/2) each is of which respectively. the other Of generated by the has 2. We order course, non-trivial the element loop of this group. 6. 7. 5. not all distinct} I (f(xl),f(x2),f(x3)) = X 0 x X 0 x X 0 - Z0, 0 M 0r + MF(2) (isomorphic E Z0}. O M r = X x X x X - Z, projection f x f x f. 36 M 0F Thus is V I x V 2 x V3 , Proof. This We where a 26-fold with each is theorem let Vi notation.

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