By Anthony Bak (auth.), Ib H. Madsen, Robert A. Oliver (eds.)
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Foliated areas glance in the neighborhood like items, yet their international constitution is usually no longer a product, and tangential differential operators are correspondingly extra complicated. within the Nineteen Eighties, Alain Connes based what's referred to now as noncommutative geometry. one of many first effects was once his generalization of the Atiyah-Singer index theorem to compute the analytic index linked to a tangential (pseudo)-differential operator and an invariant transverse degree on a foliated manifold, when it comes to topological info at the manifold and the operator.
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Extra info for Algebraic Topology Aarhus 1982: Proceedings of a conference held in Aarhus, Denmark, August 1–7, 1982
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  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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