The Connes-Chamseddine cycle and the noncommutative integral
Differential Geometry
2024-09-18 v5
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.
Keywords
Cite
@article{arxiv.2406.14300,
title = {The Connes-Chamseddine cycle and the noncommutative integral},
author = {Tong Wu and Yong Wang},
journal= {arXiv preprint arXiv:2406.14300},
year = {2024}
}