Operator K-theory

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In mathematics, operator K-theory is a variant of K-theory on the category of Banach algebras (In most applications, these Banach algebras are even C*-algebras).

Its basic feature that distinguishes it from algebraic K-theory is that it has a Bott periodicity. So there are only two K-groups, namely K₀, equal to algebraic K₀, and K₁. As a consequence of the periodicity theorem, it satisfies excision. This means that it associates to an extension of C*-algebras an exact cyclic 6-term-sequence.

Operator K-theory is a generalization of topological K-theory, defined by means of vector bundles on locally compact Hausdorff spaces.