Combinatorial 3-manifolds with 10 vertices

Abstract

We give a complete enumeration of all combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2\times S^1$ and 615 triangulations of the twisted sphere product $S^2_\times_S^1$. All the 3-spheres with up to 10 vertices are shellable, but there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.

9 pages, minor revisions, to appear in Beitr. Algebra Geom

References in corpus (3)

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
• Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds
• Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I

Cited by in corpus (11)

• A non-partitionable Cohen-Macaulay simplicial complex
• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
• Surface realization with the intersection edge functional
• Invariants of Random Knots and Links
• Parameterized Complexity of Discrete Morse Theory
• Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I
• Realizability and inscribability for simplicial polytopes via nonlinear optimization
• Minimal Triangulations of Manifolds
• Random collapsibility and 3-sphere recognition
• Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds
• Average Betti numbers of induced subcomplexes in triangulations of manifolds