An enumeration of combinatorial 3-manifolds with nine vertices

Combinatorial 3-Manifolds with 10 Vertices

We give a complete enumeration of 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×S and 615 triangulations of the twisted sphere product S×S. All the 3-spheres with up to 10 vertices are shellable, but there are 29 vertexminimal non-shellable 3-balls with 9 vertices.

Neighborly combinatorial 3-manifolds with 9 vertices

Triangulated Manifolds with Few Vertices: Combinatorial Manifolds

Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds

The understanding and classification of (compact) 3-dimensional manifolds (without boundary) is with no doubt one of the most prominent tasks in topology ever since Poincaré’s fundamental work [88] on ≪l’analysis situs≫ appeared in 1904. There are various ways for constructing 3-manifolds, some of which that are general enough to yield all 3-manifolds (orientable or nonorientable) and some that...

Positively Curved Combinatorial 3-Manifolds

We present two theorems in the “discrete differential geometry” of positively curved spaces. The first is a combinatorial analog of the Bonnet-Myers theorem: • A combinatorial 3-manifold whose edges have degree at most five has edgediameter at most five. When all edges have unit length, this degree bound is equivalent to an angle-deficit along each edge. It is for this reason we call such space...