# On two chain models for the gravity operad

## TL;DR

This paper discusses two chain-level models of the gravity operad, proving their formality and isomorphism in homology, thus clarifying their algebraic structures and relationships.

## Contribution

It introduces and compares two chain models of the gravity operad, establishing their formality and homological equivalence.

## Key findings

- Both models are formal.
- The two models have isomorphic homology.
- The models are proven to be equivalent at the chain level.

## Abstract

In this note we recall the construction of two chain level lifts of the gravity operad, one due to Getzler-Kapranov and one due to Westerland. We prove that these two operads are formal and that they indeed have isomorphic homology.