Geodesic
$K$-homology of $C^*$-algebras
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 533-540

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A functor algebraically dual to the operator $K$-functor is constructed on the category of $C^*$-algebras, and the author shows that it defines a homology theory on this category. The author also proves that it coincides with Kasparov's homology $K$-functor on a large class of $C^*$-algebras, including commutative $C^*$-algebras. This functor is used to describe a class of homotopy invariant higher signatures. Bibliography: 10 titles. 
@article{SM_1988_59_2_a15,
     author = {V. M. Manuilov},
     title = {$K$-homology of $C^*$-algebras},
     journal = {Sbornik. Mathematics},
     pages = {533--540},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_59_2_a15/}
}
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V. M. Manuilov. $K$-homology of $C^*$-algebras. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 533-540. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a15/