In a lens space of order a knot representing an element of the fundamental group of order contains a connected orientable surface properly embedded in its exterior such that intersects the meridian of minimally times. Assume has just one boundary component. Let be the minimal genus of such surfaces for , and assume . Then with respect to the genus one Heegaard splitting of , has bridge number at most .
"Small genus knots in lens spaces have small bridge number." Algebr. Geom. Topol. 6 (4) 1519 - 1621, 2006. https://doi.org/10.2140/agt.2006.6.1519