Refined topological strings on local ℙ^2

We calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on ℙ^2 (the local ℙ^2 ). The refined topological vertex formalism can not be directly applied to local ℙ^2 therefore we use the properties of the refined Hopf link to define a new two legged vertex which together with the refined vertex gives the partition function of the local ℙ^2 .