Pan Peng. A Simple Proof of Gopakumar-Vafa Conjecture for Local Toric Calabi-Yau Manifolds. Communications in Mathematical Physics. 2007.
Abstract
We prove Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds. It is also proven that the local Gopakumar-Vafa invariants of a given class vanish at large genera.