Formal formality of the hypercommutative algebras of low dimensional Calabi-Yau varieties

TL;DR

This paper investigates the algebraic structures on the cohomology of Calabi-Yau varieties, showing that for certain cases, including all Calabi-Yau 3-folds, the simplified hypercommutative algebra retains all essential information.

Contribution

It proves that the truncation of the homotopy hypercommutative algebra to a strict form is information-preserving for specific Calabi-Yau varieties, notably all Calabi-Yau 3-folds.

Findings

Truncation preserves information for some Calabi-Yau varieties.

All Calabi-Yau 3-folds exhibit formality in their hypercommutative algebra structures.

The result supports the mathematical realization of the genus zero B-model.

Abstract

There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi-Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutative algebra is well-known as a mathematical realization of the genus zero B-model. It is shown that this truncation loses no information for some cases, including all Calabi-Yau 3-folds.