Maulik and Toda recently proposed a mathematical definition of Gopakumar-Vafa(GV) invariants, which count one-dimensional torsion sheaves on a Calabi-Yau 3-fold(CY3), and is conjectually equivalent to other curve counting invariants such as Gromov-Witten invariants (GV/GW correspondence conjecture).One of the mysterious features of the GV invariants is the so-called cohomological chi-independence, which is expected from the GV/GW correspondence. In this talk, I will explain backgrounds and recent developments on the GV theory, including my joint work with Tasuki Kinjo (Tokyo), on the cohomological chi-independence for certain non-compact CY3s.