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 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 definite Siegel modular kinds of genus and degrees above two.- L.G. Lewis, Jr.: The RO(G)-graded equivariant usual 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 attached manifolds with no S1-symmetry.- P. Vogel: 2 x 2 - matrices and alertness to hyperlink concept.

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

Example text

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. The Burnside ring Mackey functor A is the unit for •. 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 case We define observe that [F(2): F(4)] = 29 . 1) below. F(2) m F D F(4), abelian 2-group, and hence so is We wish A = F, and F(2)/F(4) Here [F(2): F] = 2 6 , is an elementary F(2)/F. the topology of these spaces MA for A. In [LWI] , [LW2] we proved the following theorem in case A = F(2) (see also [G]). I. a) Hi(M A) = 0 b) The map for c) for i is an epimorphism Hi(~ A u OA) --+ Ni(MA) i < 6. H4(M A) cycles has a basis consisting of algebraic (so, in p a r t i c u l a r , position of H *(M~) , d) odd.

Four, let us consider follows: Pl (1,0,2,0) there (0,0,1,0) at Pl (I,0,0,0) and 2 and orbit here. lines PI' of of a typical element Pl of it acts as (I,0,0,2) (I,2,0,0), (1,0,2,2,) and and (I,2,0,2). ) classes Then adding at level classes (1,2,2,0), classes , giving 4 orbits. two equivalence 2 equivalence and Pl On the four equivalence acts trivially are the action are also 8 lines level are 8 orbits of the so there has 4 orbits on these. may check, on the first four, and tran- classes of lines over (l,0,O,0) Interchanging (1,2,2,2,), On lines over F.

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