The Gopakumar–Vafa invariants are numbers deﬁned as certain linear combinations of the Gromov–Witten invariants. We prove that the GV invariants of a toric Calabi–Yau threefold are integers and that the invariants for high genera vanish. The proof of the integrality is based on elementary number theory and that of the vanishing uses the operator formalism and the exponential formula.
Cite this article
Yukiko Konishi, Integrality of Gopakumar–Vafa Invariants of Toric Calabi–Yau Threefolds. Publ. Res. Inst. Math. Sci. 42 (2006), no. 2, pp. 605–648DOI 10.2977/PRIMS/1166642118