Dan Kucervosky - An abstract Brown-Douglas-Fillmore absorption theorem, I

A common generalization is given of all previous absorption theorems for -algebra extensions. We consider extensions of a stable, nuclear, separable -algebra by an arbitrary separable -algebra, and in this setting, we give a simple intrinsic criterion for an extension to be absorbing. The criterion involves only the -algebra of the extension, together with the canonical closed two-sided ideal. This is joint work with George Elliott.