Representable E-theory for Co(X)-algebras

Details Representable E-theory for Co(X)-algebras Representable E-theory for Co(X)-algebras

2000-06-23

arxiv.org/abs/math/0006182v2

Journal of Functional Analysis, 177 (2000) 178-202

Mathematics

Operator Algebras

For journal version, see http://www.idealibrary.com/links/doi/10.1006/jfan.2000.3654

Scientific paper

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, these groups are naturally isomorphic to Kasparov's representable KK-theory groups RKK(X;A,B). Applications and examples are also discussed.

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