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

**Example text**

SoX~l)) × Aj f _ _is It has an open cone bundle over In fact, it is a product bundle and %7e may write N as N of [4] S £-I × A j ~£-i × AJ 45 (17) with (SoX~i) x [I,0] x (S~-IxaJ)/~ (S x~Di) o x 0 as the cone vertex c . Set Nt = (S x ~ i) × t x o Nit,o} (18) N (t, 0 ] for o < t rel ~ < i . fl = produce a homotopy of f = ~ . closed simplex Proof. that and f is homotopic to fliN[ ~,o] fl is a homeomorphism. re! ~ . Since It follows from g is Combining these two ho~1otopies, we ~tl~E is ht (o < t < I ) o f a homeomorphism, ht(q-l(AJ))~ q h such that htl~_E = id -1 ~j ) for each of ~ .

24 R E F E R E N C E S [BM] S. Bentzen: groups. Bentzen: A. Fr6hlich: Aarhus Locally A. Fr6hlich: angew. (1976) [Ha] H. Hasse: Aarhus of certain Universitet results on space (1982). forms. (1982). free modules over arithmetic Math. (1975) 274/75 and Galois J. Reine (1982). module angew. orders. 112-124. structure Math. for 286/87 380-440. Uber die K l a s s e n z a h l Akademie [HM] Universitet obstruction Universitet Arithmetic tame extensions. Aarhus Preprint, Some numerical J. Reine [F2] Preprint, finiteness groups.

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. Rees, Novikov's conjecture and manifolds fibering over nonpositively curved manifolds, Thesis, Univ.

### 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.)

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