On a computer recognition of 3-manifolds

1997/03/26 by Sergei Matveev, Sergei V. Matveev, Matveev, Sergei V.
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.GT

paper · pdf · doi:10.48550/arxiv.math/9703211

arxiv created 1997/03/26 · openalex publication_date 1997/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe theoretical backgrounds for a computer program that recognizes all closed orientable 3-manifolds up to complexity 8. The program can treat also not necessarily closed 3-manifolds of bigger complexities, but here some unrecognizable (by the program) 3-manifolds may occur.

Citations

• The Geometries of 3-Manifolds

Related

• Algorithms in 3-manifold theory
• Algorithmic construction and recognition of hyperbolic 3-manifolds, links, and graphs
• 3-Manifolds with complexity at most 9
• Recognizing geometric 3-manifold groups using the word problem
• Computing closed essential surfaces in 3-manifolds