For 1-manifolds in R^2, vineyard monodromy on small loops arises precisely when the loop intersects a singularity of the distance function on the symmetry set.
NP–hard problems naturally arising in knot theory.Transactions of764 the American Mathematical Society, Series B, 8(15):420–441, May 2021
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The Singular Source of Vineyard Monodromy
For 1-manifolds in R^2, vineyard monodromy on small loops arises precisely when the loop intersects a singularity of the distance function on the symmetry set.