From Topology to Noncommutative Geometry: K-theory

2014/08/06 by de Silva, Nadish
#46L80 (Primary) 46L85 #58B34 #Category Theory (math.CT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1408.1170

Abstract

We associate to each unital C^*-algebra A a geometric object---a diagram of topological spaces representing quotient spaces of the noncommutative space underlying A---meant to serve the role of a generalized Gel'fand spectrum. After showing that any functor F from compact Hausdorff spaces to a suitable target category can be applied directly to these geometric objects to automatically yield an extension F which acts on all unital C^*-algebras, we compare a novel formulation of the operator K₀ functor to the extension K of the topological K-functor.

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