Three-Dimensional Pseudomanifolds on Eight Vertices
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 cla...
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/254637 |
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| author | Basudeb Datta Nandini Nilakantan |
| author_facet | Basudeb Datta Nandini Nilakantan |
| author_sort | Basudeb Datta |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cca81053fb734843af1154f556066779 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
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| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cca81053fb734843af1154f5560667792025-02-03T01:31:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/254637254637Three-Dimensional Pseudomanifolds on Eight VerticesBasudeb Datta0Nandini Nilakantan1Department of Mathematics, Indian Institute of Science, Bangalore 560 012, IndiaDepartment of Mathematics & Statistics, Indian Institute of Technology, Kanpur 208 016, IndiaA 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.http://dx.doi.org/10.1155/2008/254637 |
| spellingShingle | Basudeb Datta Nandini Nilakantan Three-Dimensional Pseudomanifolds on Eight Vertices International Journal of Mathematics and Mathematical Sciences |
| title | Three-Dimensional Pseudomanifolds on Eight Vertices |
| title_full | Three-Dimensional Pseudomanifolds on Eight Vertices |
| title_fullStr | Three-Dimensional Pseudomanifolds on Eight Vertices |
| title_full_unstemmed | Three-Dimensional Pseudomanifolds on Eight Vertices |
| title_short | Three-Dimensional Pseudomanifolds on Eight Vertices |
| title_sort | three dimensional pseudomanifolds on eight vertices |
| url | http://dx.doi.org/10.1155/2008/254637 |
| work_keys_str_mv | AT basudebdatta threedimensionalpseudomanifoldsoneightvertices AT nandininilakantan threedimensionalpseudomanifoldsoneightvertices |