Genus zero Gopakumar–Vafa type invariants for Calabi–Yau 4-folds by Cao, Yalong, Maulik, Davesh, Toda, Yukinobu

“…In analogy with the Gopakumar–Vafa conjecture on CY 3-folds, Klemm and Pandharipande defined GV type invariants on Calabi–Yau 4-folds using Gromov–Witten theory and conjectured their integrality. In this paper, we propose a sheaf-theoretic interpretation of their genus zero invariants using Donaldson–Thomas theory on CY 4-folds. …”
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Gopakumar–Vafa invariants via vanishing cycles by Maulik, Davesh, Toda, Yukinobu

“…We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov–Witten theory and Pandharipande–Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. …”
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