Examples of geodesic ghor algebras on hyperbolic surfaces

Cancellative dimer algebras on a torus have many nice algebraic and homological properties. However, these properties disappear for higher genus surfaces. We consider new class of quiver surfaces, called 'geodesic ghor algebras', that reduce to cancellative torus, yet continue These exhibit rich interplay between their central geometry the topology surface. show (nontrivial) geodesic do in fact exist, give explicit descriptions geometry. This article serves companion 'A generalization hyperbolic surfaces', where main statement is proven.