# The Fulton Mac Pherson operad and the W-construction

## TL;DR

This paper details the construction of an $O(n)$-equivariant isomorphism between the Fulton Mac Pherson operad and its W-construction, clarifying their topological operad structures.

## Contribution

It provides a detailed construction of an equivariant isomorphism between the Fulton Mac Pherson operad and the Boardman-Vogt W-construction.

## Key findings

- Established an $O(n)$-equivariant isomorphism between $F_n$ and $WF_n$
- Clarified the topological operad structures involved
- Enhanced understanding of operad equivalences in topology

## Abstract

In this short note we explain in detail the construction of a $O(n)$-equivariant isomorphism of topological operads $F_n \cong WF_n$ , where $F_n$ is the Fulton Mac Pherson operad and $W$ is the Boardman-Vogt construction