A normal form for curved differentials guarantees (4n-2)-complex structures from n-nilpotent curvature and gives Lipschitz control on persistent homology barcodes.
Mayer, A new homology theory i & ii, Annals of Mathematics 43 (1942) 370–380, 594–605
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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.