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On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8727-2169
University of Western Ontario, Canada.
2017 (English)In: JOURNAL OF GEOMETRY AND PHYSICS, ISSN 0393-0440, Vol. 111, 126-141 p.Article in journal (Refereed) Published
Abstract [en]

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. (C) 2016 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2017. Vol. 111, 126-141 p.
Keyword [en]
Noncommutative differential geometry; Chern-Gauss-Bonnet theorem; Levi-Civita connection; Riemannian curvature; Noncommutative 4-sphere
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Identifiers
URN: urn:nbn:se:liu:diva-134071DOI: 10.1016/j.geomphys.2016.10.016ISI: 000390501800009OAI: oai:DiVA.org:liu-134071DiVA: diva2:1068915
Note

Funding Agencies|Swedish Research Council

Available from: 2017-01-26 Created: 2017-01-22 Last updated: 2017-01-26

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