Combinatorial zeta functions counting triangles
Abstract
Abstract In this paper, we compute special values of certain combinatorial zeta functions counting geodesic paths in the ‐skeleton of a triangulation of an ‐dimensional manifold. We show that they carry a topological meaning. As such, we recover the first Betti and ‐Betti numbers 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.
Fields of Study & Subjects
Topological and Geometric Data Analysis
Data Management and Algorithms
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Journal of Topology
- Publisher
- Wiley
- Volume
- 19
- Issue
- 2
- Publication date
- 1 June 2026
- Language
- EN