# Homotopy Gerstenhaber Structures and Vertex Algebras

@article{Glvez2010HomotopyGS, title={Homotopy Gerstenhaber Structures and Vertex Algebras}, author={I. G{\'a}lvez and V. Gorbounov and Andrew Tonks}, journal={Applied Categorical Structures}, year={2010}, volume={18}, pages={1-15} }

We provide a simple construction of a G ∞ -algebra structure on an important class of vertex algebras V, which lifts the Gerstenhaber algebra structure on BRST cohomology of V introduced by Lian and Zuckerman. We outline two applications to algebraic topology: the construction of a sheaf of G ∞ algebras on a Calabi–Yau manifold M, extending the operations of multiplication and bracket of functions and vector fields on M, and of a Lie ∞ structure related to the bracket of Courant (Trans Amer…

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