  We propose a class of toric Lagrangian A-branes on the resolved conifold that
is suitable to describe torus knots on S^3. The key role is played by the
SL(2,Z) transformation, which generates a general torus knot from the unknot.
Applying the topological vertex to the proposed A-branes, we rederive the
colored HOMFLY polynomials for torus knots, in agreement with the Rosso and
Jones formula. We show that our A-model construction is mirror symmetric to the
B-model analysis of Brini, Eynard and Marino. Comparing to the recent proposal
by Aganagic and Vafa for knots on S^3, we demonstrate that the disk amplitude
of the A-brane associated to any knot is sufficient to reconstruct the entire
B-model spectral curve. Finally, the construction of toric Lagrangian A-branes
is generalized to other local toric Calabi-Yau geometries, which paves the road
to study knots in other three-manifolds such as lens spaces.
