A reconstruction theorem for almost-commutative spectral triples

Details A reconstruction theorem for almost-commutative spectral triples A reconstruction theorem for almost-commutative spectral triples

2011-01-31

arxiv.org/abs/1101.5908v3

Physics

Mathematical Physics

AMS-LaTeX, 18 pp. V3: Final version, to appear in Letters in Mathematical Physics. Section 2.3 has been rewritten for clarity,

Scientific paper

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.

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