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 yes Siegel modular kinds 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 out 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

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.

Again with char ~ ~ 2) H5(~FU @r ) --+ H5(MF' ~F u OF) --+ H4(~ F u OF) --+ H4(M F) 32 The first of these groups plex surfaces, = HI(M~) is zero, as ~ u 0F is a union of I and the second is isomorphic to by Alexander duality. I b)). dim H4(MF) = 79, there. putations showed last map is an eplmorphism This follows from the compu- dim HI(M ) = 27, and dim H4(~FU O F) We shall see below how to make these last two com- (cf. 2). Now let A/F act on this short exact We sequence. again obtain a short exact sequence 0--+ HI(M~) A/F --+ H4(~ F u 0r)A/r--+ H4(M~) A/F--+ 0 which is nothing other than the sequence 0 --+ HI(M~) --+ H4(3 A u @A ) --+ H4(M ~) --+ 0 as desired.

For the following untwisted number of equivalence classes of lines at level [A: F] Generators of A/F 1 Pl 40 4 PI' P2 32 4 PI' ql 33 4 PI' q2 29 8 PI' P2' P3 28 8 PI' P2' ql 25 8 PI' P2' q3 23 64 PI' P2' P3' ql' q2' q3 15 the action of of course must know the latter. 6 (and there are 54 of them). A/F and bi is as stated: on lines at level They are given by are defined mod 2 F we [LW3], theorem Recall they arise as follows: There are 15 lines at level 2, given by ai the 54 2 To determine A A, Number of equlvalence class@s - Proof.

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