Stability conditions and Teichmüller space
arXiv:2112.07912 · doi:10.1007/s00208-024-02852-6
Abstract
We consider a 3-Calabi-Yau triangulated category associated to an ideal triangulation of a marked bordered surface. Using the theory of harmonic maps between Riemann surfaces, we construct a natural map from a component of the space of Bridgeland stability conditions on this category to the enhanced Teichmüller space of the surface. We describe a relationship between the central charges of objects in the category and shear coordinates on the Teichmüller space.
65 pages. Version 2: Minor changes