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arXiv · 1209.4832

Real structures on almost-commutative spectral triples

Branimir Ćaćić
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Abstract

We refine the reconstruction theorem for almost-commutative spectral triples to a result for real almost-commutative spectral triples, clarifying, in the process, both concrete and abstract definitions of real commutative and almost-commutative spectral triples. In particular, we find that a real almost-commutative spectral triple algebraically encodes the commutative *-algebra of the base manifold in a canonical way, and that a compact oriented Riemannian manifold admits real (almost-)commutative spectral triples of arbitrary KO-dimension. Moreover, we define a notion of smooth family of real finite spectral triples and of the twisting of a concrete real commutative spectral triple by such a family, with interesting KK-theoretic and gauge-theoretic implications.

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Branimir Ćaćić. 2013-02-10. Real structures on almost-commutative spectral triples. https://doi.org/10.1007/s11005-013-0616-7

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