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The Meridional Rank Conjecture asks whether the bridge number of a knot in$S^3$ is equal to the minimal number of meridians needed to generate thefundamental group of its complement. In this paper we investigate the analogousconjecture for knotted surfaces in $S^4$. Towards this end, we give aconstruction to produce classical knots with quotients sending meridians toelements of any finite order and which detect their meridional ranks. Weestablish the equality of bridge number and meridional rank for these knots andknotted spheres obtained from them by twist-spinning. On the other hand, weshow that the meridional rank of knotted spheres is not additive underconnected sum, so that either bridge number also collapses, or meridional rankis not equal to bridge number for knotted spheres. We also show a relationshipbetween the bridge numbers of welded knots and ribbon tori using the Tube map,and give applications to bridge trisections of knotted surfaces.

Bridge numbers and meridional ranks of knotted surfaces and welded knots