A simplicial version of the 2-dimensional Fulton-MacPherson operad

Abstract

We define an operad in Top, called ${\text{FM}}_2^W$. The spaces in ${\text{FM}}_2^W$ come with CW decompositions, such that the operad compositions are cellular. In fact, each space in ${\text{FM}}_2^W$ is the realization of a simplicial set. We expect, but do not prove here, that ${\text{FM}}_2^W$ is isomorphic to the 2-dimensional Fulton-MacPherson operad ${\text{FM}}_2$. Our construction is connected to the author's work on the symplectic $(A_{\infty },2)$-category, and suggests a strategy toward equipping the symplectic cochain complex with the structure of a homotopy Batalin-Vilkoviskiy algebra.

17 pages, 10 figures. Four definitions are recalled from arXiv:1709.00119. Revised in response to referee report

References in corpus (1)

• 2-associahedra