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Non-existence of 6-dimensional pseudomanifolds with complementarity

Abstract

In a previous paper the second author showed that if MM is a pseudomanifold with complementarity other than the 6-vertex real projective plane and the 9-vertex complex projective plane, then MM must have dimension ≥6\geq 6, and - in case of equality - MM 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.Comment: 11 pages. To appear in Advances in Geometr

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