  In this article, we prove the conjecture that Kodaira-Spencer theory for the
topological 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 the
topological vertex in a vertex operator approach. We propose a conjecture of
the correlation function identity which in a degenerate case becomes Zhou\rq{}s
identity for a Hopf link.
