Kimura–Voronov–Zuckerman completion conjecture for topological vertex operator algebras

Let $V$ be a topological vertex operator algebra, and let an appropriate topological completion mean the completion of $V$ required in the cited construction. A genus-zero topological conformal field theory is the genus-zero field-theoretic structure used to construct homotopy Gerstenhaber algebras. Kimura–Voronov–Zuckerman's conjecture. An appropriate topological completion of $V$ has a structure of a genus-zero topological conformal field theory. If true, this would provide a route to the homotopy Gerstenhaber structure conjectured for topological vertex operator algebras, since the latter structure is known for genus-zero topological conformal field theories. The paper treats the statement as a conjecture and uses its geometric and operadic results in this context.