Donaldson-Thomas trasnsformations of moduli spaces of G-local systems

Understand

Kontsevich and Soibelman defined Donaldson-Thomas invariants of a 3d Calabi-Yau category equipped with a stability condition.

• Any cluster variety gives rise to a family of such categories.
• Their DT invariants are encapsulated in a single formal automorphism of the cluster variety, called the DT-transformation.
• Let S be an oriented surface with punctures, and a finite number of special points on the boundary considered modulo isotopy.