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.
Algorithms for recognizing knots and 3-manifolds
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.
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cs.CG 1years
2026 1verdicts
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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.