Representable E-theory for Co(X)-algebras, by Efton Park and Jody Trout

Let X be a locally compact space, and let A and B be Co(X)-algebras. We define the notion of an asymptotic Co(X)-morphism from A to B and construct representable E-theory groups RE(X;A,B). These are the universal groups on the category of separable Co(X)-algebras that are Co(X)-stable, Co(X)-homotopy-invariant, and half-exact. If A is RKK(X)-nuclear (in the sense of Bauval), these groups are naturally isomorphic to Kasparov's representable KK-theory groups RKK(X;A,B). Applications to families of elliptic differential operators parametrized by X, defining "fundamental classes" for unital Co(X)-algebras, and defining invariants for central bimodules in noncommutative geometry and physics are also discussed.

This paper has been published as Journal of Functional Analysis, 177 (2000) 178-202 and the preprint has been removed.

Efton Park <>
Jody Trout <>