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A Reconstruction Theorem for Almost-Commutative Spectral Triples

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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.

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  1. Department of Mathematics, California Institute of Technology, MC 253-37, 1200 E., California Blvd., Pasadena, 91125, CA, USA

    Branimir Ćaćić

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  1. Branimir Ćaćić
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Ćaćić, B. A Reconstruction Theorem for Almost-Commutative Spectral Triples. Lett Math Phys 100, 181–202 (2012). https://doi.org/10.1007/s11005-011-0534-5

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