Three dimensional pseudomanifolds on eight vertices

dc.creatorDatta, Basudeb
dc.creatorNilakantan, Nandini
dc.date2007-01-01
dc.date2008-07-18
dc.date.accessioned2026-07-07T09:51:05Z
dc.date.available2026-07-07T09:51:05Z
dc.descriptionA 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 $d \geq 3$. 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 ($B^3_9$ in Example 7 below) which does not allow any proper bistellar moves.
dc.description19 pages, Revised version. To appear in the `International Journal of Mathematics and Mathematical Sciences'
dc.identifierhttps://arxiv.org/abs/math/0701038
dc.identifierhttp://arxiv.org/abs/math/0701038
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165165
dc.subjectGeometric Topology
dc.subjectCombinatorics
dc.subject57Q15; 57Q05; 57N05; 55M25
dc.titleThree dimensional pseudomanifolds on eight vertices
dc.typetext

Files

Collections