Topological Applications of p-Adic Divergence and Gradient Operators
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914840968167424 |
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| author | Bradley, Patrick Erik |
| author_facet | Bradley, Patrick Erik |
| contents | $p$-Adic divergence and gradient operators are constructed giving rise to $p$-adic vertex Laplacian operators used by Zúñiga in order to study Turing patterns on graphs, as well as their edge Laplacian counterparts. It is shown that the Euler characteristic of a finite graph can be expressed via traces of certain heat kernels associated with these new operators. This result is applied to the extraction of topological information from Mumford curves via heat kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06439 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Applications of p-Adic Divergence and Gradient Operators Bradley, Patrick Erik Analysis of PDEs Algebraic Geometry Number Theory 35P10, 14H25 $p$-Adic divergence and gradient operators are constructed giving rise to $p$-adic vertex Laplacian operators used by Zúñiga in order to study Turing patterns on graphs, as well as their edge Laplacian counterparts. It is shown that the Euler characteristic of a finite graph can be expressed via traces of certain heat kernels associated with these new operators. This result is applied to the extraction of topological information from Mumford curves via heat kernels. |
| title | Topological Applications of p-Adic Divergence and Gradient Operators |
| topic | Analysis of PDEs Algebraic Geometry Number Theory 35P10, 14H25 |
| url | https://arxiv.org/abs/2406.06439 |