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Book Review
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Book Information
Author(s):
Kjeld Knudsen Jensen and Klaus Thomsen
Title:
Elements of $KK$-theory
Additional book information:
Mathematics: Theory \& Applications, Birkh\"auser, Boston, Basel, and Berlin, 1991, viii + 202 pp., US$49.50. ISBN 0-8176-3496-7, ISBN 3-7643-3496-7
References:
- [ABS]
- M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology \textbf{3} (1964), 3--38.
- [AH]
- M. F. Atiyah and F. Hirzebruch, \emph{Vector bundles and homogeneous spaces}, Proc. Sympos. Pure Math., vol. 3, Amer. Math. Soc., Providence, RI, 1961 pp.~7--38.
- [AS]
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. {\rm I}, Ann. of Math. (2) \textbf{87} (1968), 484--530.
- [B]
- B. Blackadar, $K$-Theory for operator algebras, Math. Sci. Res. Inst. Publ., vol. 5, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, and Tokyo, 1986.
- [BDF]
- L. G. Brown, R. G. Douglas, and P. Fillmore, Extensions of C*-algebras and $K$-homology, Ann. of Math. (2) \textbf{105} (1977), 265--324.
- [CS]
- A. Connes and G. Skandalis, The longitudinal index theorem for foliations, Publ. Res. Inst. Math. Sciences (Kyoto) \textbf{20} (1984), 1139--1183.
- [F]
- T. Fack, $K$-th\'eorie bivariante de Kasparov, S\'eminaire Bourbaki, 1982--83, expos\'e no.~605, Ast\'erisque \textbf{105--106} (1983), 149--166.
- [HS]
- M. Hilsum and G. Skandalis, Morphismes $K$-orient\'es d'espaces de feuilles et fonctorialit\'e en th\'eorie de Kasparov, Ann. Sci. \'Ecole Norm. Sup. (4) \textbf{20} (1987), 325--390.
- [K1]
- G. G. Kasparov, Topological invariants of elliptic operators, {\rm I:} $K$-homology, Izv. Akad. Nauk SSSR Ser. Mat. \textbf{39} (1975), 796--838.
- [K2]
- G. G. Kasparov, The operator $K$-functor and extensions of $\roman C^*$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. \textbf{44} (1980), 571--636.
- [K3]
- G. G. Kasparov, Equivariant $KK$-theory and the Novikov conjecture, Invent. Math. \textbf{91} (1988), 147--201.
- [L]
- C. Lance, Review of \cite {B}, Bull. Amer. Math. Soc. \textbf{18} (1988), 67--73.
- [MF]
- A. S. Mi\v s\v cenko and A. T. Fomenko, The index of elliptic operators over $\roman C^*$-algebras, Izv. Akad. Nauk SSSR Ser. Mat. \textbf{43} (1979), 831--859.
Additional Information:
Reviewer(s):
Jonathan
Rosenberg
Review Information:
Journal:
Bull. Amer. Math. Soc.
28
(1993),
342-347.
DOI:
10.1090/S0273-0979-1993-00361-6
PII:
S 0273-0979(1993)00361-6
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