Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds

Abstract

We explicitly construct small triangulations for a number of well-known 3-dimensional manifolds and give a brief outline of some aspects of the underlying theory of 3-manifolds and its historical development.

48 pages, 18 figures

References in corpus (4)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Period three actions on the three-sphere
• 3-Manifolds from Platonic Solids

Cited by in corpus (7)

• Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
• Combinatorial 3-manifolds with 10 vertices
• Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I
• Combinatorial properties of the K3 surface: Simplicial blowups and slicings
• Graph coloring manifolds
• Minimal Triangulations of Manifolds
• Average Betti numbers of induced subcomplexes in triangulations of manifolds