The K-homology of nets of C*-algebras

Giuseppe Ruzzi, Ezio Vasselli
October 29, 2014
Let X be a space, intended as a possibly curved spacetime, and A a precosheaf of C*-algebras over 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.
open access link Journal of Geometry and Physics 86 (2014) 476-491
%%% contains utf-8, see: %%% add \usepackage[utf8]{inputenc} to your latex preamble @article{Ruzzi:2014sca, author = "Ruzzi, Giuseppe and Vasselli, Ezio", title = "{The K -homology of nets of C∗ -algebras}", journal = "J. Geom. Phys.", volume = "86", year = "2014", pages = "476-491", doi = "10.1016/j.geomphys.2014.10.003", eprint = "1312.2944", archivePrefix = "arXiv", primaryClass = "math.OA", SLACcitation = "%%CITATION = ARXIV:1312.2944;%%" }

Nets of C*-algebras, K-homology, QFT on curved spacetimes