Algebraic Topology and Transformation Groups: Proceedings of - download pdf or read online

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

ISBN-10: 3540460365

ISBN-13: 9783540460367

ISBN-10: 3540505288

ISBN-13: 9783540505280

Contents: S. Bauer: The homotopy form 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 different types 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 feedback 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

Sample text

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. We shall morphism. Of course In order representing also the to given do Lemmn non-trlvial with V G Pi' identify our (and of hence this to elements pi,qi,ri of a "Dehn twist" Pl = I + 2 00 0O 0 0 V we need elements) P2 = I + 2 specific matrices of These G.

0, = • o T h e most effective way to visualize tIGS is to display FIGS a 0 for various a on a coordinate plane in which the horizontal and vertical coordinates specify lete[ and lad respectively. 2 below, the zero values of HeS* 0 are indicated by blanks. T h e only values in this plot with odd horizontal coordinate are the R_ and L_ on the horizontal axis and the (7//2} in the fourth quadrant. • . 2. - (7//2) (~/2) ... (7//2) (7//2) ... (~12) (~12) ... (~/2) (7//2) ... H~S ° for p = 2. Even though the representation ring of G is much more complicated when p :/= 2, I-I~S ° is completely determined by the integers a and ]o~GI except in the special case where Isl = c~c ---- 0.

If these disks are all even dimensional and are attached in the proper order, then the equivariant ordinary cohomology H~X of X is a free RO(G)-graded module over the equivariant ordinary eohomology of a point. 1 that if V is a complex G-representation and P(V) is the associated complex projective space with the induced linear G-action, then P(V) has the required type of cell structure. 9, which describe the ring structure of H~P(V), follow from the freeness of H~P(V). As a sample of these results, assume that p = 2 and V 54 is a complex G-representation consisting of countably many copies of both the (complex) one-dimensional sign representation ,~ and the one dimensional trivial representation 1.

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Algebraic Topology and Transformation Groups: Proceedings of a Conference held in Göttingen, FRG, August 23–29, 1987 by Stefan Bauer (auth.), Tammo tom Dieck (eds.)


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