# The K-homology of nets of C*-algebras

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

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@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;%%"
}

Keywords:

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