The C(X)-algebra of a net and index theory
  Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(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 C(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. 
Giuseppe Ruzzi, Ezio Vasselli
math.OA math-ph math.KT math.MP