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

TL;DR

This paper proves a conjectural relationship between Gopakumar-Vafa invariants of fiber classes on Calabi-Yau 4-folds and their fibers, under certain assumptions, advancing understanding in enumerative geometry.

Contribution

It establishes a proof of a conjecture linking invariants of the total space and fibers of Calabi-Yau 4-folds, under orientation compatibility.

Findings

Proves the Cao-Maulik-Toda conjecture for fiber classes

Relates invariants of Calabi-Yau 4-folds to those of fibers

Provides conditions under which the correspondence holds

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.