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 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 yes Siegel modular types 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 feedback 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 idea.

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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

Now consider of the subspace subspace tations the action of is a sum of of G, and type 0 is I, of type R of on which copies of it is easy Pl Pl 32 of on R. 1, the dimension trivially is 55. 64 irreducible to see that the number 1 is 7, of type 2 is 5, etc. 1 yields for all the subgroups 9 9 18 3 18 1 7 5 I0 I 6 2 m0 i 5 3 4 1 2 0 m1 1 6 3 6 0 0 0 m2 1 5 2 5 0 2 1 m3 1 3 3 0 I 0 0~ m4 I 4 1 2 0 0 0 m5 i 3 i 2 0 i 0 I 0 0 0 0 0 0 (consistent) / m6 system has rank 7, and hence a unique (mo,ml, ....

1. 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.

Note that R0(G ) is the quotient of R0(G) obtained by allowing the obvious cancellations and that RO0(G ) is the quotient of R0(G ) obtained by identifying conjugate representations. Let A be the irreducible complex representation which sends the standard generator of 7//p to e 2'~i/p. The monoid R0(G) is generated by elements of the form Am _ An where 1 < m , n _< p - 1 . Define a homomorphism from R0(G) to 77, regarded as a monoid under multiplication, by sending the generator Am - An to m(n-1), where n -1 denotes the unique integer such that 1 _< n -1 _< p - 1 and n(n - 1 ) - 1 mod p.

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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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