2 6 N ov 1 99 9 Asymptotically split extensions and E - theory Vladimir
نویسنده
چکیده
We show that the E-theory of Connes and Higson can be formulated in terms of C∗extensions in a way quite similar to the way in which the KK-theory of Kasparov can. The essential difference is that the role played by split extensions should be taken by asymptotically split extensions. We call an extension of a C∗-algebra A by a stable C∗algebra B asymptotically split if there exists an asymptotic homomorphism consisting of right inverses for the quotient map. An extension is called semi-invertible if it can be made asymptotically split by adding another extension to it. Our main result is that there exists a one-to-one correspondence between asymptotic homomorphisms from SA to B and homotopy classes of semi-invertible extensions of S2A by B.
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