On the Chern–Gauss–Bonnet theorem for the noncommutative 4-sphere

We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization...

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Veröffentlicht in:Journal of geometry and physics 2017-01, Vol.111, p.126-141
Hauptverfasser: Arnlind, Joakim, Wilson, Mitsuru
Format: Artikel
Sprache:eng
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Zusammenfassung:We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern–Gauss–Bonnet type theorem for the noncommutative 4-sphere.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2016.10.016