Hochschild cohomology of graded gentle algebras and intrinsic formality

TL;DR

This paper computes the Hochschild cohomology of graded gentle algebras, including algebraic structures, and applies these results to Fukaya categories and formality characterization.

Contribution

It provides a detailed description of Hochschild cohomology for graded gentle algebras, linking it to Fukaya categories and formality properties.

Findings

Hochschild cohomology of graded gentle algebras is explicitly described.

Connections established between Hochschild cohomology and Fukaya categories.

Characterization of intrinsically formal graded gentle algebras under mild conditions.

Abstract

We describe the (bigraded) Hochschild cohomology of graded gentle algebras along with the Gerstenhaber bracket and cup product. In particular, this yields a description of the Hochschild cohomology of partially wrapped Fukaya categories of surfaces in the sense of Haiden-Katzarkov-Kontsevich which have at least one stop. Our results are an important ingredient in the author's recent description of the derived Picard group of partially wrapped Fukaya categories and graded gentle algebras. As another application we provide a characterisation of intrinsically formal graded gentle algebras under mild assumptions.