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[B~r2q-l, BU], q > 1 < n>Z is s u r j e c t i v e . Proof. We h a v e to m a k e s u r e t h a t t h e r e a r e no o b s t r u c t i o n s f o r e x t e n d i n g up t o homotopy a given map B~Zq-l~ 0: B ~ Z q - l ' ~ BU Byr2q C B ~ 2q+l ~ 1]T I , s t e p b y s t e p o v e r t h e s e q u e n c e of s k e l e t o n s : .... C_ lira Byrn = Byr . qT~ 1 n , BU The extension [3].

6] Atiyah, M . F . , 433. T h e index of elliptic operators I, to appear. , A fixed point t h e o r e m for nilpotent Lie groups; Proc. A . M . S . 9 (1958), 822 - 823. [8] Auslander, L. , O n the Euler characteristic of c o m p a c t complete locally affine spaces I, C o m m e n t . Math. Helv. ; II, Bull. A . M . S . 67 (1961), 405 - 406. , T h e structure of complete locally affine manifolds; Topology 3 (1964), 131 - 139. [lO] Auslander, L. and M a r k u s , L. , H o l o n o m y of flat affinely connected manifolds, Ann.

95 Vol. -B. Brinkmann und D. Puppe, Kategorien und Funktoren. XlI, 107 Seiten. 1966. 00 Vol. 4: M Arkowitz and C. R. Curjel, Groups of Homotopy Classes. 2nd. revised edition. IV, 36 pages. 1967. 20 Vol. 19: G. Stolzenberg, Volumes, Limits and Extensions of Analytic Varieties. IV, 45 pages. 1966. -P. Serre, Cohomologie Galoisienne. Troisi~me ~dition. VIII, 214 pages. 1965. 50 Vol. 20: R. Hartshorne, Residues and Duality. VIII, 423 pages. 1966. 00 Vol. 6: H. Hermes, Eine ]'ermlogik mit Auswahloperator.

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