Lian–Zuckerman homotopy Gerstenhaber conjecture for topological vertex operator algebras

A topological vertex operator algebra is the algebraic structure considered in the paper, and a homotopy Gerstenhaber algebra is the corresponding higher-algebraic structure introduced in the cited framework. Lian–Zuckerman's conjecture. A topological vertex operator algebra gives a homotopy Gerstenhaber algebra. The conjecture refines the earlier observation that the cohomology of a strong topological chiral algebra has a Batalin–Vilkovisky algebra structure. In the paper, this conjecture is proved using the geometric and operadic formulation developed there; genus-zero topological conformal field theories were already known to yield homotopy Gerstenhaber algebras.