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.
Topological persistence vineyard for803 dynamic functional brain connectivity during resting and gaming stages.Journal of Neuroscience Methods,804 267:1–13, July 2016
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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.