Léo Bénard, Yann Chaubet, Nguyen Viet Dang, Thomas Schick
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.