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Representable E-Theory for C0(X)-Algebras

✍ Scribed by Efton Park; Jody Trout

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 241 KB
Volume: 177
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3654

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✦ Synopsis

Let X be a locally compact space, and let A and B be C 0 (X)-algebras. We define the notion of an asymptotic C 0 (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 C 0 (X)-algebras that are C 0 (X)-stable, C 0 (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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