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

ISBN-10: 3540129022

ISBN-13: 9783540129028

ISBN-10: 354038782X

ISBN-13: 9783540387824

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

**Sample text**

Of Math. Studies 88, Princeton [ lO ] Iniv. Press, 1977. A. S. M i ~ e n k o , Infinite-dimensional representations of discrete groups and higher signature. 38 SSSR Ser. Math. ~974), 81-106. [ 11 ] , Topology, Aarhus 1978, [ 12] Izv. Akad. Nauk. C*-algebra and K-theory, Algebraic Springer-Verlag Lecture Notes in Math. 763. P. 0rlik, Seifert manifolds, Lecture Notes in Math. 291 ~972), Springer-Verlag. [ 13] M. S. Raghunathan, Discrete subgroups of Lie groups, Ergebnisse der Math. under ihrer ~enzgebiete 68 [ l~] ~972), Springer Verlag.

There is a map If X Sing(X) ~ (X)et, X = BGLn(C), Since the map X there is a sim- is a scheme of finite type over (Z/p) Sing(X) ~ holim(Z/p)~(X)et. cial scheme space inducing a homotopy equivalence Applying this for the simpli- we get a map Sing(X) ~ (X)et the following commutative diagram C, (BGLn(Z/I)6) ÷ ~ (BUn) ~. is natural in X, we have 36 BGLn(Z ) 6 x Sing(C) , BGLn(Z ) S i n g (BGL n (C)) It f o l l o w s BGL in n (C) ^ p n, that we o b t a i n that determine map id: Proof by the (BGLn(Z/£)6)+ map.

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. using R~ G the p r o d u c t in the u s u a l construction let GLn(R) be the way. where scheme over = SpecA matrices BGLn(R) schould which set.

### Algebraic Topology Aarhus 1982: Proceedings of a conference held in Aarhus, Denmark, August 1–7, 1982 by Anthony Bak (auth.), Ib H. Madsen, Robert A. Oliver (eds.)

by Anthony

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