Categorification of Donaldson-Thomas invariants via Perverse Sheaves

TL;DR

This paper constructs a perverse sheaf on moduli spaces of stable sheaves on Calabi-Yau 3-folds, providing a new mathematical foundation for Gopakumar-Vafa invariants via categorification.

Contribution

It introduces a perverse sheaf that lifts to a mixed Hodge module on moduli spaces, enabling a rigorous mathematical definition of Gopakumar-Vafa invariants.

Findings

Perverse sheaf constructed on moduli space of stable sheaves.

Lifts to a mixed Hodge module, enriching the cohomology theory.

Provides a mathematical framework for Gopakumar-Vafa invariants.

Abstract

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.