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KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras.

2 votes
1 answer
179 views

Différences between KKO and KKR in Kasparov theory

In Kasparov article : The operator K functor and extensions of $C^*$algebras there is the definition of the two bifunctors $KKO : ralg^{op} \times ralg \to Ab$ and $KKR : Ralg^{op}_r \times Ralg_r \to …
InfiniteLooper's user avatar
1 vote

Homotopy equivalence of Kasparov's $KK$-Theory

It is really the same thing as for ordinary homotopy. Mainly a concatenation. I will write for a space $X$, $XB$ the algebra of continous functions from $X$ to $B$. All the other notations follow th …
InfiniteLooper's user avatar
5 votes
1 answer
498 views

reference for KK theory

I wanted to ask you, if you have any good references (book or pdf) to learn about the KK theroy of Kasparov. I think the presentation of Blackadar is too close from the commutative theory. I was sea …
InfiniteLooper's user avatar