Every link in a 3-manifold with a one-sided Heegaard splitting is isotopic to a non-orientable plat closure of a surface braid, with explicit examples in lens spaces and trivial circle bundles.
Bredon and John W
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Knots and non-orientable surfaces in 3-manifolds
Every link in a 3-manifold with a one-sided Heegaard splitting is isotopic to a non-orientable plat closure of a surface braid, with explicit examples in lens spaces and trivial circle bundles.