Gopakumar-Vafa invariants of fiber classes on Calabi-Yau 4-folds fibered over curves

Abstract

We prove a conjectural correspondence of Cao-Maulik-Toda which relates Gopakumar-Vafa invariants of fiber classes on a smooth projective Calabi-Yau 4-fold fibered over a curve to the Gopakumar-Vafa invariants of a smooth fiber under an orientation compatibility assumption on the moduli spaces.

32 pages. Material largely rewritten, we delete the part on Hilbert schemes as the original proof in version 1 contains a gap