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.
How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms
2 Pith papers cite this work. Polarity classification is still indexing.
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Canopies generalize vines and vineyards by tracking simplex pairs in filtered chain complexes instead of persistence diagram points, with proofs of homeomorphism and applications to multiplicity and monodromy.
citing papers explorer
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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.
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Canopies: A Generalization of Vines and Vineyards for Parameterized Persistence
Canopies generalize vines and vineyards by tracking simplex pairs in filtered chain complexes instead of persistence diagram points, with proofs of homeomorphism and applications to multiplicity and monodromy.