A normal form for curved differentials guarantees (4n-2)-complex structures from n-nilpotent curvature and gives Lipschitz control on persistent homology barcodes.
Brzeziński, Curved differential graded algebras and corings, Bulletin of the Belgian Mathematical Society - Simon Stevin 20 (2013)
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Operational Calculus on Curved Differentials: Optimal N-Complex Bounds and Persistent Homology
A normal form for curved differentials guarantees (4n-2)-complex structures from n-nilpotent curvature and gives Lipschitz control on persistent homology barcodes.