A new spectral-DGLA method preserves L-infinity structure through cohomology and re-proves formality for gentle algebras.
Deformations of Gentle $A_\infty$-Algebras
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In this paper we calculate the Hochschild cohomology of gentle $A_\infty$-algebras of arc collections on marked surfaces without boundary components. When the underlying arc collection has no loops or two-cycles, we show that the dgla structure of the Hochschild complex is formal and give an explicit realization of all deformations up to gauge equivalence.
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$ L_\infty $-spectral sequences for Hochschild cohomology
A new spectral-DGLA method preserves L-infinity structure through cohomology and re-proves formality for gentle algebras.