By Stefan Bauer (auth.), Tammo tom Dieck (eds.)
Contents: S. Bauer: The homotopy kind of a 4-manifold with finite basic 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 sorts 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 attached manifolds with out S1-symmetry.- P. Vogel: 2 x 2 - matrices and alertness to hyperlink thought.
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Extra info for Algebraic Topology and Transformation Groups: Proceedings of a Conference held in Göttingen, FRG, August 23–29, 1987
Proof. If A is untwisted, W I x W2 x W 3 with W i c V i. 15, we see that M r is rational, and indeed, 0 * this theorem shows that MF, a Zariski open set in Mr, is isomorphic But then theorem to M~ a Zariski open x ~, in X x X x X = ~ x ~ x ~. is isomorphic to a Zariski open set in (X/WI) x (X/W2) x (X/W3) , x ~ set so MA which is itself isomorphic is rational. Then by [AM, proposition I], H,(M A) is torsion-free. to 52 References [AM] Artin, M. and Mumford, D. Some elementary examples of unirational varieties which are not rational, Proc.
Some elementary examples of unirational varieties which are not rational, Proc. Lond. Math. Soc. 25 (1972), 75-95. [B] Bredon, G. Introduction to compact transformation Academic Press, New York, 1972. [G] van der Geer, G. On the geometry of a Siegel modular threefold, Math. Ann. 260 (1982), 317-350. [LW I ] Lee, R. and Weintraub, S. H. Cohomology of a Siegel modular variety of degree two, in Group Actions on Manifolds, R. , Amer. Math. , Providence, RI, 1985, 433-488. [LW2] Cohomology of Sp4(Z) and related groups and spaces, Topology 24 (1985), 291-310.
Case A/F generated by PI" Here the covering space is has 4 components as f-l(0) u f-I u f-l(~) Now the 6-tuple is X × X x X. F-l(*,x,y) P has cardinality 4 in giving the first entry. The second and third are as in a). P, The fourth and fifth entries are the number of components of the inverse image of the diagonal in is the quotient of X x X. But this inverse image P (as in a)) by the group generated by p x id: X x X--+ X x X, X and this quotient has two components. The sixth entry is as in a).