학술논문
Combinatorial zeta functions counting triangles
Document Type
Working Paper
Source
Subject
Language
Abstract
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.
Comment: 17 pages, comments welcome
Comment: 17 pages, comments welcome