  We show that there is a perverse sheaf on a fine moduli space of stable
sheaves on a smooth projective Calabi-Yau 3-fold, which is locally the perverse
sheaf of vanishing cycles for a local Chern-Simons functional, possibly after
taking an etale Galois cover. This perverse sheaf lifts to a mixed Hodge module
and gives us a cohomology theory which enables us to define the Gopakumar-Vafa
invariants mathematically.
