Download Algebraic K-Theory: Proceedings of a Conference Held at by Anthony Bak (auth.), R. Keith Dennis (eds.) PDF

By Anthony Bak (auth.), R. Keith Dennis (eds.)

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Extra info for Algebraic K-Theory: Proceedings of a Conference Held at Oberwolfach, June 1980 Part II

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Write contains a cofinal sequence. r r U(A,G) = ~ V~. and let W t = i ~IV~ . i=l cofinal. let Recall that components of Certainly Wt+ I = W I ~)W t. ~ Y. Then Z ~ Y' ~)Y 1 For H C ~ is a groupoid. We claim that G and an A-free H-fixed Y C {Wt} U(A,G), as an A[H]-space and Z' ~ Z ~ W t as an A[G]- H space for appropriate Y' and Z' in U(A,G) and some t, hence (Z' ~ Y') G Y ~ W t. 6. It would not be useful ~IB(G,GL(n,A)) with respect GL(n,A) + GL(n+I,A). sequence {A t } to form the telescope to the maps induced by the inclusions This would amount to replacing of trivial representations.

P:H + GL(n,A), topological For each homomorphism (re+n,A,G) and is equivalent G-monoid as a Hopf G-space B~(A,G). let A n denote P the corresponding A[H]- and choose an H-isomorphism i P There exists morphism :An + V C U(A,G) n. P P such a Vp since U(A,G) x = gH ~ G/H, let xVp = gYp. contains to be the following XVp = gYp g ~ Vp qp(h) = (o¢)(h)q; the K-module = (gf,qp) by v(p,x) as in Remark fioqi-lp :V + fV p o = XVp. 2, define i q ~- Ano¢ = AnO by ¢(h) = f-lhf and o ~ Vo q ¢ GL(n,A) thus q may be viewed as an H-isomorphism A~ G x H An .

Analysis shows that B B ~ ~0BB~ ~-bundle B~ = O(n). inherits a n the loop space on the class~ :B~ ÷ ~ B B ~ is equivalent to (B~) +. We mimic the outline just given. (G,~)-bundle p:E ÷ B. Deeper ~BB~ space B(G,~) for such (G,~)-bundles. sentations of G in ~. For a topological This is just a That is, the actions of G and H on the total space commute (we think of ~ as acting on the right and G on the left). ~O n and a G-map between G-spaces such that the action by each g c G ~-bundles. Proposition 0.

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