The Connes-Chamseddine cycle and the noncommutative integral
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913502967365632 |
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| author | Wu, Tong Wang, Yong |
| author_facet | Wu, Tong Wang, Yong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Connes-Chamseddine cycle and the noncommutative integral Wu, Tong Wang, Yong Differential Geometry 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. |
| title | The Connes-Chamseddine cycle and the noncommutative integral |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2406.14300 |