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

Bottman, Nathaniel

doi:10.2140/agt.2024.24.1183

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A simplicial version of the $2$–dimensional Fulton–MacPherson operad

Nathaniel Bottman

Algebraic & Geometric Topology 24 (2024) 1183–1202

DOI: 10.2140/agt.2024.24.1183

Abstract

We define an operad in Top, called ${FM}_{2}^{W}$ . The spaces in ${FM}_{2}^{W}$ come with CW decompositions such that the operad compositions are cellular. In fact, each space in ${FM}_{2}^{W}$ is the realization of a simplicial set. We expect, but do not prove here, that ${FM}_{2}^{W}$ is isomorphic to the $2$ –dimensional Fulton–MacPherson operad ${FM}_{2}$ . 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–Vilkovisky algebra.

Keywords

Deligne conjecture, operads, Fukaya categories, Gerstenhaber algebras, BV algebras, E2

Mathematical Subject Classification

Primary: 18M75, 55P48

Secondary: 53D37

References

Publication

Received: 2 April 2022

Revised: 27 August 2022

Accepted: 18 September 2022

Published: 12 April 2024

Authors

Nathaniel Bottman
Max Planck Institute for Mathematics Bonn Germany

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Volume 24, issue 2 (2024)