The $C(X)$-algebra of a net and index theory

Giuseppe Ruzzi, Ezio Vasselli
April 30, 2014
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.
open access link Journal of Functional Analysis 267 (2014) 112–143
@article{Ruzzi:2012wn, author = "Ruzzi, Giuseppe and Vasselli, Ezio", title = "{The C(X)-algebra of a net and index theory}", year = "2012", eprint = "1212.2801", archivePrefix = "arXiv", primaryClass = "math.OA", SLACcitation = "%%CITATION = ARXIV:1212.2801;%%" }

Keywords:
Superselection Theory, QFT on curved spacetimes, noncommutative geometry