Pseudomanifolds with Complementarity
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A simplicial complex is said to satisfy complementarity if exactly one of each complementary pair of nonempty vertex-sets constitutes a simplex of the complex. In this article we show that if there exists a n-vertex d-dimensional pseudo-manifold M with complementarity and either n≤d+6 or d≤ 6 then d = 0, 2, 4 or 6 with n = 3d/2 + 3. We also show that if M is a d-dimensional pseudo-manifold with complementarity and the number of vertices in M is ≤ d+5 then M is either a set of three points or the unique 6-vertex real projective plane or the unique 9-vertex complex projective plane.
- Arnoux, P. and Marin, A.: The Kühnel triangulation of complex projective plane from the view-point of complex crystallography (Part II), Mem. Fac. Sci. Kyushu Univ. Ser. A 45 (1991), 167–244.
- Bagchi, B. and Datta, B.: On Kühnel's 9-vertex complex projective plane, Geom. Dedicata 50 (1994), 1–13.
- Bagchi, B. and Datta, B.: A structure theorem for pseudomanifolds, Discrete Math., 188 (1998), 41–60.
- Barnette, D. and Gannon, D.:Manifolds with few vertices, Discrete Math. 16 (1976), 291–298.
- Brehm, U. and Kühnel, W.: Combinatorial manifolds with few vertices, Topology 26 (1987), 465–473.
- Brehm, U. and Kühnel, W.: 15-vertex triangulation of an 8-manifold, Math. Annal. 294 (1992), 167–193.
- Datta, B.: Combinatorial manifolds with complementarity, Proc. Indian Acad. Sci. (Math. Sci.) 104 (1994), 385–388.
- Datta, B.: Minimal triangulation, complementarity and projective planes, In: Geometry from the Pacific Rim, Gruyter, Berlin, 1997, pp. 77–84.
- Eells, J. and Kuiper, N. H.: Manifolds which are like projective planes, Publ. Math. IHES 14 (1962), 181–222.
- Hartsfield, N. and Ringel, G.: Clean triangulations, Combinatorica 11 (1991), 145–155.
- Kühnel, W.: Triangulations of manifolds with few vertices, In: F. Tricerri (ed.). Advances in Differential Geometry and Topology, World Scientific, Singapore, 1990, pp. 59–114.
- Kühnel, W. and Banchoff, T. F.: The 9-vertex complex projective plane, Math. Intell. 15(3) (1983), 11–22.
- Pseudomanifolds with Complementarity
Volume 73, Issue 2 , pp 143-155
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- 1. Department of Mathematics, Indian Institute of Science, Bangalore, 560 012, India; e-mail