Surfaces with binary and skew-gentle algebras

Indecomposable objects in the bounded derived category of a skew-gentle algebra have been classified by many authors in an algebraic, combinatorial or geometric way, while a description of morphisms has not been given. In this talk, we use a new geometric model, namely a graded marked surface with binary, to investigate a non-positive graded skew-gentle algebra. For any graded unknotted curve on the surface, we associate an object in the perfect derived category of the algebra, and for any oriented intersection between unknotted curves, we construct a morphism, which form a basis of the corresponding morphism space. This is based on joint work with Yu Qiu and Chao Zhang.