Let Delta be a dual polar space of rank n greate than 4, H be a hyperplane of Delta and Gamma: = Delta\setminus H be the complement of H in Delta. We shall prove that, if all lines of Delta have more than 3 points, then Gamma is simply connected. Then we show how this theorem can be exploited to prove that certain families of hyperplanes of dual polar spaces, or all hyperplanes of certain dual polar spaces, arise from embeddings.
Cardinali, I., DE BRUYN, B., Pasini, A. (2009). On the simple connectedness of hyperplane complements in dual polar spaces. DISCRETE MATHEMATICS, 309(2), 294-303 [10.1016/j.disc.2007.12.006].
On the simple connectedness of hyperplane complements in dual polar spaces
CARDINALI I.;PASINI A.
2009-01-01
Abstract
Let Delta be a dual polar space of rank n greate than 4, H be a hyperplane of Delta and Gamma: = Delta\setminus H be the complement of H in Delta. We shall prove that, if all lines of Delta have more than 3 points, then Gamma is simply connected. Then we show how this theorem can be exploited to prove that certain families of hyperplanes of dual polar spaces, or all hyperplanes of certain dual polar spaces, arise from embeddings.
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https://hdl.handle.net/11365/37732
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