Abstract
In this paper and its prequel, we give a necessary and sufficient condition for two essential simple loops on a [Formula: see text]-bridge sphere in an even Heckoid orbifold for a [Formula: see text]-bridge link to be homotopic in the orbifold. We also give a necessary and sufficient condition for an essential simple loop on a [Formula: see text]-bridge sphere in an even Heckoid orbifold for a [Formula: see text]-bridge link to be peripheral or torsion in the orbifold. The prequel treated the case when the [Formula: see text]-bridge link is a [Formula: see text]-torus link, and this paper treats the remaining cases.
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