Combinatorial manifolds with complementarity |
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Authors: | Basudeb Datta |
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Institution: | 1. Department of Mathematics, Indian Institute of Science, 560 012, Bangalore, India
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Abstract: | A simplicial complex is said to satisfy complementarity if exactly one of each complementary pair of nonempty vertex-sets constitutes a face of the complex. We show that if a d-dimensional combinatorial manifold M with n vertices satisfies complementarity then d=0, 2, 4, 8, or 16 with n=3d/2+3 and |M| is a “manifold like a projective plane”. Arnoux and Marin had earlier proved the converse statement. |
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