# Spectral sequences associated to deformations

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## Abstract

Lapin has constructed a multiplicative spectral sequence from a deformation of an \(A_{\infty }\)-algebra. In particular, as noted by the same author, one can apply this construction to a deformation induced by a filtration of an \(A_{\infty }\)-algebra. A question that naturally appears is whether this latter multiplicative spectral sequence is isomorphic to the one that is canonically associated to the filtration and that typically appears in basic textbooks on homological algebra. We provide a positive answer to the previous question and we also explain the interesting constructions of Lapin in more structural terms.

## Keywords

Homological algebra Spectral sequences Dg algebras \(A_{\infty }\)-algebras## Mathematics Subject Classification

14D15 16E45 16S80 16W70 18G40 18G55 55T05## References

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