By Anthony Bak (auth.), Ib H. Madsen, Robert A. Oliver (eds.)

**Read Online or Download Algebraic Topology Aarhus 1982: Proceedings of a conference held in Aarhus, Denmark, August 1–7, 1982 PDF**

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**Extra resources for Algebraic Topology Aarhus 1982: Proceedings of a conference held in Aarhus, Denmark, August 1–7, 1982**

**Example text**

14], H*(SJ;Z/2) ~ H*(SO;Z/2) = im(~*). ]. , for instance by looking at the Serre spectral sequence of the fibration BU ~ BSO ~ Spin. We c l a i m that if of algebras, a*: H*(BSO;Z/2) fixing the subalgebra standard B o c k s t e i n map, then P a* ~ H*(BSO;Z/2) is any map and c o m m u t i n g with the is an isomorphism. But this is an easy c o n s e q u e n c e of the two relations ~2i+1 = w2i+1 + decomposable; sqlw2i = w2i+1. Finally, we will show that T h e o r e m 2 implies T h e o r e m 1.

Oriented m a n i f o l d and discrete follows from Theorem A. Then, Let us now recall the so-called Novikov's Let (~i~,wl~#)~ > h . be given as above. g x id: is hpmotopic , in [ 2], the following corollary M n = X/F equiyalence where Then~ the surgery map. be 6iven as above. conjecture conjecture [ I0] [ ll] that the conjecture is valid if w is true. is true for any At times it was also claimed by is the fundamental linear ana C 40 group of ~erely) a non-positively out in the critique Mn is not closed.

The maps F! and F" are defined using an algebraic version of integration along the fibre for line bundles. the case of group rings the isomorphism F! [WI] chap. C, [C-SI] and explicit in [H]. In is implicit in The general case is due to Ranicki (after some prodding by us). 6 and the appendix by Ranicki in [H-T-W]). By combining F! i) Twisting Diagram for f : (R,~o,U) + (S,m,u) Yf! Ln(S,a,a) = Ln(S,y~,u) f! L (S,~,u) n = Ln(S,Y~,-~) Ln(R,a0,u) /\ (R,ao,a) Ln-2 = Ln(R,~0,-u) /\ Ln+l(f ! ) /--,, Ln+l(S,a,u) ~f!