By Anthony Bak (auth.), Ib H. Madsen, Robert A. Oliver (eds.)
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Extra resources for Algebraic Topology Aarhus 1982: Proceedings of a conference held in Aarhus, Denmark, August 1–7, 1982
Ideas by Quillen, (Z prime # p) K(Z) Friedlander defines a homotopy (BGL(Z/i) +) ~ BU A. 2. 1 is the homotopy We note tive diagram, that a map lifting since commutes K(Z) I ~ PB, up to homotopy. 2 with a b u t m e n t of this map to a c e r t a i n equivalent for --~ BU A P £ = p, K(Z/£)~ to is the homoin BU A. P covering The space JK(Z)~. )et) G face ~ G G = GLn(R). Spec R the More defined over the x G Spec R > maps special precisely, schemes We can GL over over that formula, be the one this pro-simplicial As of the N o e t h e r i a n BG is d e f i n e d to n.
P ^ ( B G L ( Z / i ) + ) p ~ BU ^ P The m a p BU^ ~ BUa . 6. From definition groups (BGL n (C)) et to the is, above ~- et PB. 2 A JK(Z)p. From finding the c o n s t r u c t i o n a homotopy an e l e m e n t of between KI(sG) = 0. 8 is 37 REFERENCES [I] BSkstedt, M. and Waldhausen, to appear. , Stable real cohomology of arithmetic groups, Ann. Ecole Norm. (4) 7 (1974), 235-272. , Computations of K-theories of finite fields, Topology 15(1976), 87-109. of Math. Studies, Princeton University Press (1982) .
Extends to S £-I* (S x D i) o (~5) S £-I*(S × D i) 0 Corresponding to S £-I* (So×~_+~)l) ~ S £-I* (S ×~)I) there are two sub-bundles O of (14): (16) S£-I, (So×~_+Di) Each of these fibration is left invariant by hl~+E 2n+i ~+~n+i h such that hl~_E 2n+i = id and is a homeomorphism. We need the following lemma. 1 Le__~t f: (s~-l*(so×Di)) × a j (S£-I* (So×Di)) × A j he a homotopy equivalence such that is a homeomor~hism with f-I (~) = B . homotopic to a homeomorlohism tel Proof. (of. _ff £ + dim S o + i + j _> 5 , then fl8 .