A normal form for curved differentials guarantees (4n-2)-complex structures from n-nilpotent curvature and gives Lipschitz control on persistent homology barcodes.
Pauksztello, Homological epimorphisms of differential graded algebras, Com- munications in Algebra 37 (2009) 2337–2350
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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.