On the simple connectedness of hyperplane complements in dual polar spaces, II
نویسندگان
چکیده
Suppose ∆ is a dual polar space of rank n and H is a hyperplane of ∆. Cardinali, De Bruyn and Pasini have already shown that if n ≥ 4 and the line size is greater than or equal to four then the hyperplane complement ∆ −H is simply connected. This paper is a follow-up, where we investigate the remaining cases. We prove that the hyperplane complements are simply connected in all cases except three specific types of hyperplanes occuring in the smallest case, when the rank and the line size are both three.
منابع مشابه
On the simple connectedness of hyperplane complements in dual polar spaces
Let ∆ be a dual polar space of rank n ≥ 4, H be a hyperplane of ∆ and Γ := ∆\H be the complement of H in ∆. We shall prove that, if all lines of ∆ have more than 3 points, then Γ 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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عنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010