2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52304We calculate the topological string amplitudes of Calabi-Yau toric threefolds corresponding to 4D, N=2, SU(2) gauge theory with N_f=0,1,2,3,4 fundamental hypermultiplets by using the method of the geometric transition and show that they reproduce Nekrasov's formulas for instanton counting. We also determine the asymptotic forms of the Gopakumar-Vafa invariants of the Calabi-Yau threefolds including those at higher genera from instanton amplitudes of the gauge theory.25 pages, 5 figures; (v2) eq.(10) correctedHigh Energy Physics - Theorytext