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<p>In Connes and Chamseddine (J Geom Phys 57(1):1–21, 2007) defined a cycle in the general framework of noncommutative geometry. They computed this cycle for the Dirac operator on 4-dimensional 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 Figueroa et al. (J Geom Phys 26(3–4):329–339, 1998) by the normal coordinated way on n-dimensional manifolds. As a corollary, the Connes–Chamseddine cycle on 6-dimensional manifolds is obtained.</p>

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The Connes–Chamseddine Cycle and the Noncommutative Integral

  • 期刊论文

  • 发表日期：

    2025年1月7日

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  • Tong Wu,
  • Yong Wang

摘要

In Connes and Chamseddine (J Geom Phys 57(1):1–21, 2007) defined a cycle in the general framework of noncommutative geometry. They computed this cycle for the Dirac operator on 4-dimensional 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 Figueroa et al. (J Geom Phys 26(3–4):329–339, 1998) by the normal coordinated way on n-dimensional manifolds. As a corollary, the Connes–Chamseddine cycle on 6-dimensional manifolds is obtained.