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.
The computational complexity of classical knot761 recognition.Journal of Knot Theory and Its Ramifications, 32(11), October 2023
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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.