@phdthesis{oai:nagoya.repo.nii.ac.jp:00006172, author = {Minabe, Satoshi and 三鍋, 聡司}, month = {Mar}, note = {We give two new results on Gromov-Witten invariants of Calabi-Yau threefolds. The first one is a computation of local Gromov-Witten invariants of cubic surfaces at all genera. We give an explicit formula for the generating function of these invariants in a closed form. The second one is on the flop invariance of Gromov-Witten invariants of toric Calabi-Yau threefolds. We prove transformation formulas for generating functions of Gromov-Witten invariants on general toric Calabi-Yau threefolds under flops. Both results are based on the theory of the topological vertex. We present proofs of these two results together with required background on Gromov-Witten invariants. This paper has been accepted as the author’s doctoral thesis at the Graduate School of Mathematics, Nagoya University (defended in March 2007)., 名古屋大学博士学位論文 学位の種類:博士(数理学)(課程) 学位授与年月日:平成19年3月23日}, school = {名古屋大学, Nagoya University}, title = {Topological vertex and its applications}, year = {2007} }