2020/10/27 by Clément Maria, Maria, Clément, Owen Rouillé +1 · 1 citation
Computer Science · #Computability, Logic, AI Algorithms #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2010.14316
openalex publication_date 2020/10/27 · openalex created_date 2021/04/13 · openalex updated_date 2026/07/28
Quantum topological invariants have played an important role in computational topology, and they are at the heart of major modern mathematical conjectures. In this article, we study the experimental problem of computing large r values of Turaev-Viro invariants TVr. We base our approach on an optimized backtracking algorithm, consisting of enumerating combinatorial data on a triangulation of a 3-manifold. We design an easily computable parameter to estimate the complexity of the enumeration space, based on lattice point counting in polytopes, and show experimentally its accuracy. We apply this parameter to a preprocessing strategy on the triangulation, and combine it with multi-precision arithmetics in order to compute the Turaev-Viro invariants. We finally study the improvements brought by these optimizations compared to state-of-the-art implementations, and verify experimentally Chen and Yang's volume conjecture on a census of closed 3-manifolds.