Beschreibung:
By adapting the algebraic notion of universal connection to the setting of unbounded KK-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of smooth algebras and a notion of dfferentiable C_-module. The theory of operator spaces provides the required tools. Finally, the above mentioned KK-cycles with connection can be viewed as the morphisms in a category whose objects are spectral triples.