SEMI-INVERTIBLE EXTENSIONS AND ASYMPTOTIC HOMOMORPHISMS

@article{Manuilov2003SEMIINVERTIBLEEA,
  title={SEMI-INVERTIBLE EXTENSIONS AND ASYMPTOTIC HOMOMORPHISMS},
  author={V. Manuilov and K. Thomsen},
  journal={K-theory},
  year={2003},
  volume={32},
  pages={101-138}
}
We consider the semigroup Ext(A, B) of extensions of a separable C � -algebra A by a stable C � -algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group Ext 1/2 (A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext 1/2 (A, B) is homotopy invariant and that it coincides with the functor of homotopy classes of asymptotic homomorphisms from C(T) ⊗ A to M(B) that map SA ⊆ C(T) ⊗ A into B. 

References

SHOWING 1-10 OF 20 REFERENCES
THE OPERATOR K-FUNCTOR AND EXTENSIONS OF C*-ALGEBRAS
Algebraic K-theory of stable C∗-algebras
On non-semisplit extensions, tensor products and exactness of groupC*-algebras
C*-algebras associated with groups with Kazhdan's property T
Remark on certain *-algebra extensions considered by G. Skandalis
Elements of KK-theory
...
1
2
...