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arXiv:2112.07912 [math.GT]AbstractReferencesReviewsResources

Stability conditions and Teichmüller space

Dylan G. L. Allegretti

Published 2021-12-15, updated 2024-03-13Version 2

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.

Comments: 65 pages. Version 2: Minor changes
Categories: math.GT, hep-th, math.AG, math.DG
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