2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228937In a lens space X of order r a knot K representing an element of the fundamental group pi_1 X = Z/rZ of order s <= r contains a connected orientable surface S properly embedded in its exterior X-N(K) such that the boundary of S intersects the meridian of K minimally s times. Assume S has just one boundary component. Let g be the minimal genus of such surfaces for K, and assume s >= 4g-1. Then with respect to the genus one Heegaard splitting of X, K has bridge number at most 1.This is the version published by Algebraic & Geometric Topology on 11 October 2006Geometric Topology57M27, 57M25text