Non-existence of 6-dimensional pseudomanifolds with complementarity

Details Non-existence of 6-dimensional pseudomanifolds with complementarity Non-existence of 6-dimensional pseudomanifolds with complementarity

2004-04-12

arxiv.org/abs/math/0404225v1

Mathematics

Geometric Topology

11 pages. To appear in Advances in Geometry

Scientific paper

In a previous paper 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 $\geq 6$, 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.

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