Equivariant Gromov-Witten Theory of GKM Orbifolds
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.
Academic Commons
Zong, Zhengyu
Author
Liu, Chiu-Chu M.
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2015
eng
2017-06-12T17:39:37Z
2017-06-12T18:38:29Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D8513WZC