A Thurston compactification of the space of Bridgeland stability conditions

Contact: Daniel Huybrechts.
 

Motivated by the homological mirror symmetry and the work of Bridgeland-Smith, we investigate an analogy between the theory of Bridgeland stability conditions and Teichmuller theory. Specifically, we construct a Thurston type compactification of the space of Bridgeland stability conditions on a smooth projective curve.

We give two applications in the case of an elliptic curve. Firstly, we compare our compactification with the classical construction for a torus via the homological mirror symmetry. Secondly, we give a Nielsen-Thurston type classification of autoequivalences.

This is based on a joint work with Kohei Kikuta (Osaka) and Genki Ouchi (Nagoya).