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

Suppose ΔΔ is a dual polar space of rank nn and HH is a hyperplane of ΔΔ. Cardinali, De Bruyn and Pasini have already shown that if n≥4n≥4 and the line size is greater than or equal to 4 then the hyperplane complement Δ−HΔ−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.