On the simple connectedness of hyperplane complements in dual polar spaces, II

Suppose Δ is a dual polar space of rank n and H is a hyperplane of Δ. Cardinali, De Bruyn and Pasini have already shown that if n≥4 and the line size is greater than or equal to 4 then the hyperplane complement Δ−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 for three specific types of hyperplane occurring in the smallest case, when the rank and the line size are both 3.