$K$-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/}
}
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/