three-dimensional pseudomanifolds on eight vertices
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ID: 161197
2008
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Abstract
A normal pseudomanifold is a pseudomanifold in which the links of simplices are also pseudomanifolds. So, a normal 2-pseudomanifold triangulates a connected closed 2-manifold. But, normal d-pseudomanifolds form a broader class than triangulations of connected closed d-manifolds for d≥3. Here, we classify all the 8-vertex neighbourly normal 3-pseudomanifolds. This gives a classification of all the 8-vertex normal 3-pseudomanifolds. There are 74 such 3-pseudomanifolds, 39 of which triangulate the 3-sphere and other 35 are not combinatorial 3-manifolds. These 35 triangulate six distinct topological spaces. As a preliminary result, we show that any 8-vertex 3-pseudomanifold is equivalent by proper bistellar moves to an 8-vertex neighbourly 3-pseudomanifold. This result is the best possible since there exists a 9-vertex nonneighbourly 3-pseudomanifold which does not allow any proper bistellar moves.
| Reference Key |
datta2008internationalthree-dimensional
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|---|---|
| Authors | ;Basudeb Datta;Nandini Nilakantan |
| Journal | structural engineering and mechanics |
| Year | 2008 |
| DOI |
10.1155/2008/254637
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| URL | |
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