Thurston compactifications of spaces of stability conditions on curves (Q6567153)

Various previous works by Gaiotto, Moore, Neitzke; Bridgeland, Smith; Dimitrov, Haiden, Katzarkov, Kontsevich, and others have suggested an analogy between Teichmüller spaces (and mapping class groups) and the space of Bridgeland stability conditions (and autoequivalence groups). This paper investigates a compactification of the space of Bridgeland stability conditions as an analogue of the Thurston compactification in Teichmüller theory, specifically for the bounded derived category of coherent sheaves on smooth projective curves.\N\NThe authors utilize the mass function with respect to a stability condition to define a map from the space of stability conditions to a projective space, subsequently using it to define a compactification of the stability space. For the derived categories of elliptic curves, the authors present a trichotomy of autoequivalences (periodic, reducible, pseudo-Anosov) by examining the action of autoequivalences on the compactification. This results in the categorical analogue of the Nielsen-Thurston classification in this context.