# A formality framework for commutative deformations

## TL;DR

This paper develops a formal framework for understanding commutative deformations of algebras using Harrison cohomology, adapting Kontsevich's formality results from associative to commutative cases.

## Contribution

It introduces a Harrison cohomology-based framework for commutative deformations and extends Kontsevich's formality theorem to commutative algebras.

## Key findings

- Harrison cohomology effectively characterizes commutative deformations.
- The formality of the Harrison complex implies the deformability of commutative algebras.
- Extension of Kontsevich's results to the commutative setting.

## Abstract

In this article, we use Harrison cohomology to provide a framework for commutative deformations. In particular, Kontsevich's result that formality of (the Hochschild complex of) an associative algebra implies its deformability is adapted for commutative algebras, with the Harrison complex.