Equivariant Gromov-Witten Theory of GKM Orbifolds | Posted on:2016-06-01 | Degree:Ph.D | Type:Dissertation | University:Columbia University | Candidate:Zong, Zhengyu | Full Text:PDF | GTID:1470390017483194 | Subject:Mathematics | Abstract/Summary: | | In this paper, we study the all genus Gromov-Witten theory for any GKM orbifold X. We generalize the Givental formula which is studied in the smooth case in [41] [42] [43] to the orbifold case. Specifically, we recover the higher genus Gromov-Witten invariants of a GKM orbifold X by its genus zero data. When X is toric, the genus zero Gromov-Witten invariants of X can be explicitly computed by the mirror theorem studied in [22] and our main theorem gives a closed formula for the all genus Gromov-Witten invariants of X. When X is a toric Calabi-Yau 3-orbifold, our formula leads to a proof of the remodeling conjecture in [38]. The remodeling conjecture can be viewed as an all genus mirror symmetry for toric Calabi-Yau 3-orbifolds. In this case, we apply our formula to the A-model higher genus potential and prove the remodeling conjecture by matching it to the B-model higher genus potential. | Keywords/Search Tags: | GKM, Genus, Gromov-witten, Orbifold, Remodeling conjecture, Formula | | Related items |
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