A reconstruction theorem for almost-commutative spectral triples
Abstract
We propose an expansion of the definition of almost-commutative spectral triple that accommodates non-trivial fibrations and is stable under inner fluctuation of the metric, and then prove a reconstruction theorem for almost-commutative spectral triples under this definition as a simple consequence of Connes's reconstruction theorem for commutative spectral triples. Along the way, we weaken the orientability hypothesis in the reconstruction theorem for commutative spectral triples, and following Chakraborty and Mathai, prove a number of results concerning the stability of properties of spectral triples under suitable perturbation of the Dirac operator.
Cite
@article{arxiv.1101.5908,
title = {A reconstruction theorem for almost-commutative spectral triples},
author = {Branimir Ćaćić},
journal= {arXiv preprint arXiv:1101.5908},
year = {2012}
}
Comments
AMS-LaTeX, 19 pp. V4: Updated version incorporating the erratum of June 2012, correcting the weak orientability axiom in the definition of commutative spectral triple, stengthening Lemma A.10 to cover the odd-dimensional case and the proof of Corollary 2.19 to accommodate the corrected weak orientability axiom