Combinatorial 3-Manifolds with 10 Vertices
Please always quote using this URN: urn:nbn:de:0297-zib-9071
- 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 $S^2 x S^1$ and 615 triangulations of the twisted sphere product $S^2 \underline{x} S^1$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.
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| Author: | Frank H. Lutz |
|---|---|
| Document Type: | ZIB-Report |
| Tag: | enumeration; minimal triangulations; shellability; triangulated manifolds |
| MSC-Classification: | 57-XX MANIFOLDS AND CELL COMPLEXES (For complex manifolds, see 32Qxx) / 57Nxx Topological manifolds / 57N10 Topology of general 3-manifolds [See also 57Mxx] |
| 57-XX MANIFOLDS AND CELL COMPLEXES (For complex manifolds, see 32Qxx) / 57Qxx PL-topology / 57Q15 Triangulating manifolds | |
| Date of first Publication: | 2006/03/02 |
| Series (Serial Number): | ZIB-Report (06-14) |
| ZIB-Reportnumber: | 06-14 |
| Published in: | Appeared in: Beitr. Algebra Geom. 49, 97-106 (2008 |
