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In this article, we prove the conjecture that Kodaira-Spencer theory for thetopological vertex is a free fermion theory. By dividing the $\mathbb{C}^3$curve into core and asymptotic regions and using Boson-Fermion correspondence,we construct a generic three-leg correlation function which reformulates thetopological vertex in a vertex operator approach. We propose a conjecture ofthe correlation function identity which in a degenerate case becomes Zhou\rq{}sidentity for a Hopf link.

Vertex Operators, $\mathbb{C}^3$ Curve and Topological Vertex