Combinatorial zeta functions counting triangles
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916715895455744 |
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| author | Bénard, Léo Chaubet, Yann Dang, Nguyen Viet Schick, Thomas |
| author_facet | Bénard, Léo Chaubet, Yann Dang, Nguyen Viet Schick, Thomas |
| contents | In this paper, we compute special values of certain combinatorial zeta functions counting geodesic paths in the (n-1)-skeleton of a triangulation of a n-dimensional manifold. We show that they carry a topological meaning. As such, we recover the first Betti number and L2-Betti number of compact manifolds, and the linking number of pairs of null-homologous knots in a 3-manifold. The tool to relate the two sides (counting geodesics/topological invariants) are random walks on higher dimensional skeleta of the triangulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11226 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Combinatorial zeta functions counting triangles Bénard, Léo Chaubet, Yann Dang, Nguyen Viet Schick, Thomas Geometric Topology Algebraic Topology Combinatorics 57Q70 In this paper, we compute special values of certain combinatorial zeta functions counting geodesic paths in the (n-1)-skeleton of a triangulation of a n-dimensional manifold. We show that they carry a topological meaning. As such, we recover the first Betti number and L2-Betti number of compact manifolds, and the linking number of pairs of null-homologous knots in a 3-manifold. The tool to relate the two sides (counting geodesics/topological invariants) are random walks on higher dimensional skeleta of the triangulation. |
| title | Combinatorial zeta functions counting triangles |
| topic | Geometric Topology Algebraic Topology Combinatorics 57Q70 |
| url | https://arxiv.org/abs/2303.11226 |