The Fulton–MacPherson operad and the $W$-construction

We construct an $O(n)$-equivariant isomorphism of topological operads $F_n \cong WF_n$ where $F_n$ is the Fulton–MacPherson operad and $W$ is the Boardman–Vogt construction. For $n = 2$ the isomorphism is explicit.

Keywords

operad, $W$-construction, Fulton–MacPherson

2010 Mathematics Subject Classification

18D50, 55R80

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This work was partially supported by the EPSRC grant number EP/R014604/1 and by the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.

Received 8 August 2020

Received revised 12 September 2020

Accepted 17 September 2020

Published 24 March 2021