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

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• 作者：Joakim Arnlind^a ; ^{joakim.arnlind@liu.se} ; Mitsuru Wilson^b ; ^{mwils57@uwo.ca}
• 关键词：46L87
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：Complete
• 页码：126-141
• 全文大小：473 K
• 卷排序：111

文摘

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.