The Homeomorphism Problem For Hyperbolic Manifolds I

2021/08/02 by Joe Scull, Scull, Joe
Mathematics · #57K32 #57M #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2108.00779

openalex publication_date 2021/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a bounded runtime solution to the homeomorphism problem for closed hyperbolic 3-manifolds. This is an algorithm which, given two triangulations of hyperbolic 3-manifolds by at most t tetrahedra, decides if they represent the same hyperbolic 3-manifold with runtime bounded by 2^2^t^O(t). We do this by first finding a hyperbolic structure on each manifold given as a geometric triangulation and then comparing the two as geometric manifolds.

Citations

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds
• Strong rigidity ofQ-rank 1 lattices

Related

• Algorithmic aspects of homeomorphism problems
• Algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs
• Construction and Recognition of Hyperbolic 3-Manifolds with Geodesic Boundary
• Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds
• Homotopy Hyperbolic 3-Manifolds are Hyperbolic