Algebraic structures given by triangulations of surfaces without punctures

Thomas Brüstle

We study the quiver with potential (Q,W) which encodes a triangulation of an oriented marked surface. Homotopy classes of marked curves in the surface correspond to string modules over the Jacobian algebra J(Q,W). This provides a "categorification" of those curves, and we explicitly describe the irreducible morphisms and the Auslander-Reiten translation.