On the simple connectedness of hyperplane complements in dual polar spaces

Abstract: Let be a dual polar space of rank , be a hyperplane of and be the complement of in . We shall prove that, if all lines of have more than 3 points, then 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. [Copyright &y& Elsevier]