2024/06/20 by Tong Wu, Yong Wang, Wu, Tong +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2406.14300
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.