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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

$C^*$-algebras of proper foliations

Author(s): A. Candel
Journal: Proc. Amer. Math. Soc. 124 (1996), 899-905.
MSC (1991): Primary 46L55; Secondary 57R30, 58F09
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Abstract: We study the $C^*$-algebras of proper foliations. In case of finite depth they are described by a tower of exact sequences. We conclude with remarks about foliations almost without holonomy and AF-embeddability.


References:

1.
B. Blackadar, $K$-theory for operator algebras, Math. Sci. Res. Inst. Publ., vol. 5, Springer, New York and Berlin, 1986. MR 88g:46082

2.
A. Connes, A survey on foliations and operator algebras, Proc. Sympos. Pure Math., vol. 38, Amer. Math. Soc., Providence, RI, 1982 pp. 521--628. MR 84m:58140

3.
J. Cantwell and L. Conlon , Poincaré-Bendixson theory for leaves of codimension one, Trans. Amer. Math. Soc. 265 (1981). MR 82f:57019

4.
------, Tischler fibrations of open foliated sets, Ann. Inst. Fourier (Grenoble) 31 (1981), 113--135. MR 83e:57021

5.
T. Fack and X. Wang, The $C^*$-algebras of Reeb foliations are not AF-embeddable, Proc. Amer. Math. Soc. 108 (1990), 941--946. MR 90i:46117

6.
G. Kasparov, Hilbert $C^*$-modules: Theorems of Stinespring and Voiculesco, J. Operator Theory 4 (1980), 133--150. MR 82b:46074

7.
T. Natsume, $C^*$-algebras of codimension one foliations without holonomy, Math. Scand. 56 (1985), 96--104. MR 87b:58066

8.
M. Pimsner, Embedding some transformation group $C^*$-algebras into AF-algebras, Ergodic Theory Dynamical Systems 3 (1983), 613--626. MR 86d:46054

9.
A. M. Torpe, $K$-theory for the leaf space of foliations by Reeb components, J. Funct. Anal. 61 (1985), 15--71. MR 86h:46102


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Additional Information:

A. Candel
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: candel@math.uchicago.edu

DOI: 10.1090/S0002-9939-96-03213-3
PII: S 0002-9939(96)03213-3
Received by editor(s): October 3, 1994
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1996, American Mathematical Society


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