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The refined topological string theory was first studied by Iqbal-Kozcaz-Vafa.[2] They introduced the refined parameter t to the BPS state counting which induced the so-called refined topological vertex.Later it was found that the refinement corresponds to Nekrasovs instanton counting formula[3] as well as motivic Donaldson-Thomas invariants.[4] Recently this direction has inspired many works on the structure of quantum geometry and quantum algebra.