Geometriae Dedicata

, Volume 73, Issue 2, pp 143–155

Pseudomanifolds with Complementarity

  • Basudeb Data

DOI: 10.1023/A:1005076308582

Cite this article as:
Data, B. Geometriae Dedicata (1998) 73: 143. doi:10.1023/A:1005076308582


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.


Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Basudeb Data
    • 1
  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia; e-mail