Chern character and Fermi point
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914380342362112 |
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| author | Horie, Kyouhei |
| author_facet | Horie, Kyouhei |
| contents | This paper expresses the Chern character for topological K-theory based on the formulation of the family of Fredholm operators, by using the points at which the Fredholm operator becomes singular (Fermi points). In particular, we explain that the odd Chern character can be thought of as a generalization of the spectral flow. As applications, we give elementary proofs of the evenness of the edge index and the bulk-edge correspondence for four-dimensional topological insulators with time-reversal symmetry of class AI. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06704 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern character and Fermi point Horie, Kyouhei K-Theory and Homology Mesoscale and Nanoscale Physics Mathematical Physics Algebraic Topology 55N15, 19K56, 81V70, 81Q70 This paper expresses the Chern character for topological K-theory based on the formulation of the family of Fredholm operators, by using the points at which the Fredholm operator becomes singular (Fermi points). In particular, we explain that the odd Chern character can be thought of as a generalization of the spectral flow. As applications, we give elementary proofs of the evenness of the edge index and the bulk-edge correspondence for four-dimensional topological insulators with time-reversal symmetry of class AI. |
| title | Chern character and Fermi point |
| topic | K-Theory and Homology Mesoscale and Nanoscale Physics Mathematical Physics Algebraic Topology 55N15, 19K56, 81V70, 81Q70 |
| url | https://arxiv.org/abs/2505.06704 |