Simple connectedness of hyperplane complements in some geometries related to buildings |
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Authors: | Anna Kasikova |
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Institution: | Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA |
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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. |
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Keywords: | Building Incidence geometry Point-line space Hyperplane Simple connectedness |
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