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Non-existence of 6-dimensional pseudomanifolds with complementarity

By Bhaskar Bagchi and Basudeb Datta


Abstract. In a previous paper ([10]) the second author showed that if M is a pseudomanifold with complementarity other than the 6-vertex real projective plane and the 9-vertex complex projective plane, then M must have dimension ≥ 6, and- in case of equality- M must have exactly 12 vertices. In this paper we prove that such a 6-dimensional pseudomanifold does not exist. On the way to proving our main result we also prove that all combinatorial triangulations of the 4-sphere with at most 10 vertices are combinatorial 4-spheres

Topics: combinatorial triangulations, collapsible simplicial complexes, complementarity, piecewise-linear manifolds
Year: 2004
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