Functorial Filtrations for Semiperfect generalisations of Gentle Algebras

In this thesis we introduce a class of semiperfect rings which generalise the class of finite-dimensional gentle algebras. We consider complexes of modules over these rings which have finitely generated projective homogeneous components. We then classify them up to homotopy equivalence. The method we use to solve this classification problem is called the functorial filtrations method. The said method was previously only used to classify modules.