Operadic formulation of topological vertex algebras and Gerstenhaber or Batalin-Vilkovisky algebras

TL;DR

This paper develops an operadic framework for topological vertex algebras, providing a geometric construction of associated Batalin-Vilkovisky and Gerstenhaber algebra structures on their cohomology, linking algebraic and topological concepts.

Contribution

It introduces an operadic formulation for topological vertex algebras and constructs their algebraic structures using geometric and homological methods.

Findings

Operadic formulation of topological vertex algebras.

Construction of BV and Gerstenhaber structures on cohomology.

Connection between algebraic structures and topological operads.

Abstract

We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad).