Asymptotically split extensions and E-theory
| dc.creator | Manuilov, V. | |
| dc.creator | Thomsen, K. | |
| dc.date | 1999-11-26 | |
| dc.date.accessioned | 2026-07-07T05:31:56Z | |
| dc.date.available | 2026-07-07T05:31:56Z | |
| dc.description | 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 $S^2A$ by $B$. | |
| dc.description | 14 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/9911208 | |
| dc.identifier | http://arxiv.org/abs/math/9911208 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79484 | |
| dc.subject | Operator Algebras | |
| dc.title | Asymptotically split extensions and E-theory | |
| dc.type | text |