The Khomology of nets of C^{∗}algebras
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 Θsummable Khomology of A interpreting them in terms of the holonomy equivariant Khomology of the associated C^{∗}dynamical system. This yields a characteristic class for Khomology cycles of A with values in the odd cohomology of X, that we interpret as a generalized statistical dimension.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 December 2014
 DOI:
 10.1016/j.geomphys.2014.10.003
 arXiv:
 arXiv:1312.2944
 Bibcode:
 2014JGP....86..476R
 Keywords:

 Algebraic quantum field theory;
 Khomology;
 CheegerSimons classes;
 Mathematics  Operator Algebras;
 Mathematical Physics;
 Mathematics  KTheory and Homology
 EPrint:
 To appear in Journal of Geometry and Physics