Stability conditions and Teichm\"uller space
Geometric Topology
2024-10-08 v2 High Energy Physics - Theory
Algebraic Geometry
Differential Geometry
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 Teichm\"uller space of the surface. We describe a relationship between the central charges of objects in the category and shear coordinates on the Teichm\"uller space.
Cite
@article{arxiv.2112.07912,
title = {Stability conditions and Teichm\"uller space},
author = {Dylan G. L. Allegretti},
journal= {arXiv preprint arXiv:2112.07912},
year = {2024}
}
Comments
65 pages. Version 2: Minor changes