Holomorphic curves with boundary on an immersed Lagrangian surface can have corners, due to which they may undergo a type of bubbling that does not occur in the smooth case. I will explain an algebraic framework for eliminating this problem, which results in well-defined Floer and open Gromov-Witten theories. The main algebraic gadget is the higher genus multiplicative preprojective algebra, which can be understood as the singular fundamental group of an immersed surface. This is joint work with Georgios Dimitroglou Rizell and Tobias Ekholm.