Stability conditions and Teichm\"uller space
Dylan G. L. Allegretti
TL;DR
This paper establishes a connection between Bridgeland stability conditions on a 3-Calabi-Yau category and the enhanced Teichmüller space of a surface, linking algebraic and geometric structures.
Contribution
It constructs a natural map from stability conditions to Teichmüller space and relates central charges to shear coordinates, bridging algebraic and geometric frameworks.
Findings
Constructed a map from stability conditions to Teichmüller space.
Described the relationship between central charges and shear coordinates.
Linked harmonic map theory to stability conditions and Teichmüller 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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory