Open Gromov–Witten Theory of KP2,KP1×P1,KWP1,1,2,KF1 and Jacobi Forms.

It was known through the efforts of many works that the generating functions in the closed Gromov–Witten theory of K P 2 are meromorphic quasi-modular forms (Coates and Iritani in Kyoto J Math 58(4):695–864, 2018; Lho and Pandharipande in Adv Math 332:349–402, 2018; Coates and Iritani in Gromov–Witten invariants of local P 2 and modular forms, arXiv:1804.03292 [math.AG], 2018) basing on the B-model predictions (Bershadsky et al. in Commun Math Phys 165:311–428, 1994; Aganagic et al. in Commun Math Phys 277:771–819, 2008; Alim et al. in Adv Theor Math Phys 18(2):401–467, 2014). In this article, we extend the modularity phenomenon to K P 1 × P 1 , K W P [ 1 , 1 , 2 ] , K F 1 . More importantly, we generalize it to the generating functions in the open Gromov–Witten theory using the theory of Jacobi forms where the open Gromov–Witten parameters are transformed into elliptic variables. [ABSTRACT FROM AUTHOR]