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**

Let be the ring of Witt vectors on its algebraic closure choose (noncanonically) an ambedding I: W(F£) ~ C, W(F£) F . We the complex numbers. It is known that either R (Spec R)et is weakly contractible if is a separably closed field, or a local ring satis- fying Hensel's lemma, with separably closed residue field. 4. R = F£, C, (Friedlander or [3],[5]). BGLn(F£)et + BGLn(W(F£))et ÷ BGLn(C)et homology groups with coefficients in The Friedlander map BGLn(Z/£) 6 ~ BGLn(F£)et, The base change maps induce isomorphisms on Z/p, K(Z/£)~ ~ BU~^ beginning of this paragraph, W(F£).

Ix r This completes Remark: obstruction This = (1 , -1 , -1 ) . But this is cearly impossible. the proof of Theorem B. last example of Q(8a,b,c) shows that the finiteness presents new problems when compared to the finiteness o b s t r u c t i o n of Q(8a,b). In [BI] we saw that the plus part of o (e) could always be "made rational" for 4 groups of type Q(8a,b). The above example shows that this is not possible for groups of type Q(8a,b,c). 24 R E F E R E N C E S [BM] S. Bentzen: groups. Bentzen: A.

2] , it suffices to show that the surgery map [ MnxDi x I , ~ ; G/Top ,* ] Ln+i+l s (~i~n 'Wl ~)) is split monomorphic Let for i ! i , n + i ~ 5 S x ~ Ln+j+ 1 (~iMn,wl~n)) (9) be represented f (3) I = [0,i]) by a surgery problem (~+i+l~ ~+i+l~ ~+i+l~ wn+i+l) • + satisfying ~here the following , -- @~ x ~ix O I;M n x D i x i,}~ x D i x 0,M n x ~i x I) conditions: We do not have to assume that simpler. m+i+l Un+i = ~+wn+i+l is a simple homotopy equivalence; I is a homeomorphism. 3) h: M n x ])i hI~ s-cobordism , we may identify ~+i as may be interpreted as a simple homotopy equivalence (i0) such that Applying the 0 with respect to f+ si-i = 8~i , respectively.

### 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 William

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