Deformations of Gentle $A_\infty$-Algebras

Jasper van de Kreeke; Raf Bocklandt

Deformations of Gentle $A_\infty$-Algebras

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arxiv 2304.10223 v2 pith:M24U5EFV submitted 2023-04-20 math.RA

Raf Bocklandt , Jasper van de Kreeke This is my paper · ORCID

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keywords algebrasdeformationsgentlehochschildinftyboundarycalculatecohomology

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abstract

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
math.AT 2025-08 conditional novelty 6.0 of 10

A new spectral-DGLA method preserves L-infinity structure through cohomology and re-proves formality for gentle algebras.

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