Three-Dimensional Pseudomanifolds on Eight Vertices

Basudeb Datta and Nandini Nilakantan

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-21

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 -pseudomanifolds form a broader class than triangulations of connected closed -manifolds for . 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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:254637

DOI: 10.1155/2008/254637

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