Abstract
Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C0(X)-algebra to any precosheaf of C⁎-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov K-homology of A, and interpret them in terms, respectively, of the representation theory and the K-homology of the associated C0(X)-algebra. When A is an observable net over the spacetime X in the sense of algebraic quantum field theory, this yields a geometric description of the recently discovered representations affected by the topology of X.
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