Index Theory on Incomplete Cusp Edge Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913974146039808 |
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| author | Liu, Jayson |
| author_facet | Liu, Jayson |
| contents | We study Dirac-type operators on incomplete cusp edge spaces with invertible boundary families. In particular, we construct the heat kernel for the associated Laplace-type operator and prove that the Dirac operators are essentially self-adjoint and Fredholm on their unique self adjoint domain. Using the asymptotics of the heat kernel and a generalisation of Getzler's rescaling argument we establish an index formula for these operators including a signature formula for the Hodge-de Rham operator on Witt incomplete cusp edge spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Index Theory on Incomplete Cusp Edge Spaces Liu, Jayson Differential Geometry We study Dirac-type operators on incomplete cusp edge spaces with invertible boundary families. In particular, we construct the heat kernel for the associated Laplace-type operator and prove that the Dirac operators are essentially self-adjoint and Fredholm on their unique self adjoint domain. Using the asymptotics of the heat kernel and a generalisation of Getzler's rescaling argument we establish an index formula for these operators including a signature formula for the Hodge-de Rham operator on Witt incomplete cusp edge spaces. |
| title | Index Theory on Incomplete Cusp Edge Spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.01982 |