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

Nathaniel Bottman

Algebraic & Geometric Topology 24 (2024) 1183–1202
Abstract

We define an operad in Top, called FM 2W. The spaces in FM 2W come with CW decompositions such that the operad compositions are cellular. In fact, each space in FM 2W is the realization of a simplicial set. We expect, but do not prove here, that FM 2W is isomorphic to the 2–dimensional Fulton–MacPherson operad FM 2. Our construction is connected to the author’s work on the symplectic (A,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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