Simple connectedness of hyperplane complements in some geometries related to buildings

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.