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arXiv · 1604.01159

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

Joakim Arnlind·Mitsuru Wilson
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Abstract

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 Gauss-Chern-Bonnet type theorem for the noncommutative 4-sphere.

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BibTeXRIS

Joakim Arnlind, Mitsuru Wilson. 2016-04-05. On the Gauss-Chern-Bonnet theorem for the noncommutative 4-sphere. https://doi.org/10.1016/j.geomphys.2016.10.016

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