The Connes-Chamseddine cycle and the noncommutative integral

Tong Wu; Yong Wang

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arXiv · 2406.14300

The Connes-Chamseddine cycle and the noncommutative integral

Tong Wu·Yong Wang

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Abstract

In [5], Connes and Chamseddine defined a cycle in the general framework of noncommutative geometry. They computed this cycle for the Dirac operator on 4-dimensioanl manifolds. We propose a way to study the Connes-Chamseddine cycle from the viewpoint of the noncommutative integral on 6-dimensional manifolds in this paper. Furthermore, we compute several interesting noncommutative integral defined in [8] by the normal coodinated way on n-dimensional manifolds. As a corollary, the Connes-Chamseddine cycle on 6-dimensional manifolds is obtained.

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Tong Wu, Yong Wang. 2024-06-20. The Connes-Chamseddine cycle and the noncommutative integral. https://arxiv.org/abs/2406.14300

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