Simple connectedness of hyperplane complements in some geometries related to buildings

  • Authors:

  • Anna Kasikova

  • Affiliations:

  • Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

For a class of parapolar spaces that includes the geometries E"6","4, E"7","7, and E"8","1 with lines of size at least three, the metasymplectic spaces with lines of size at least four, and the polar line Grassmannians with lines of size at least four except D"4","2(3), we show that the subgraph of the point-collinearity graph induced on the complement of a hyperplane is simply connected. We also show that these parapolar spaces have Veldkamp lines.