2007/01/01 by Basudeb Datta, Datta, Basudeb, Nandini Nilakantan +1
Computer Science · Mathematics · #55M25 #57N05 #57Q05 #57Q15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #Topological and Geometric Data Analysis #math.CO #math.GT #msc:55M25 #msc:57N05 #msc:57Q05 #msc:57Q15
paper · pdf · doi:10.48550/arxiv.math/0701038
19 pages, Revised version. To appear in the `International Journal of Mathematics and Mathematical Sciences'
openalex publication_date 2007/01/01 · arxiv created 2008/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 73 such 3-pseudomanifolds, 38 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 non-neighbourly 3-pseudomanifold (B39 in Example 7 below) which does not allow any proper bistellar moves.