Geometrically fibred two-knots (Q1121559)

We show that no cyclic branched cover of an r-twist spin of a nontrivial prime, simple classical knot with \(r>2\) is reflexive (determined by its complement). (Modulo the Poincaré conjecture, all fibred 2-knots with closed fibre having a geometric structure and monodromy of finite order are cyclic branched covers of twist spins of such knots). On the other hand, if a fibred 2-knot has closed fibre a coset space of the 3- dimensional Lie group ``Nil'' and the monodromy is of infinite order then, excepting one pair, the knot is reflexive.