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Simple connectedness of hyperplane complements in some geometries related to buildings
Authors:Anna Kasikova
Institution:Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA
Abstract:For a class of parapolar spaces that includes the geometries E6,4, E7,7, and E8,1 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 D4,2(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.
Keywords:Building  Incidence geometry  Point-line space  Hyperplane  Simple connectedness
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