Pseudomanifolds with complementarity

Data, Basudeb (1998) Pseudomanifolds with complementarity. In: Geometriae Dedicata, 73 (02). pp. 143-155.

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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 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 less than or equal to d less than or equal to + 6 or d less than or equal to 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 less than or equal to 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. Mathematics Subject Classification (1991): 57Q15.

Item Type:	Journal Article
Publication:	Geometriae Dedicata
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	pseudomanifolds;triangulation;complementarity.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	29 Dec 2009 08:31
Last Modified:	19 Sep 2010 05:26
URI:	http://eprints.iisc.ac.in/id/eprint/19106

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