The K-homology of nets of C*-algebras
arXiv:1312.2944 · doi:10.1016/j.geomphys.2014.10.003
Abstract
Let X be a space, intended as a possibly curved spacetime, and A a precosheaf of C*-algebras on X. Motivated by algebraic quantum field theory, we study the Kasparov and Theta-summable K-homology of A interpreting them in terms of the holonomy equivariant K-homology of the associated C*-dynamical system. This yields a characteristic class for K-homology cycles of A with values in the odd cohomology of X, that we interpret as a generalized statistical dimension.
To appear in Journal of Geometry and Physics