Fixing a set ϵ of generators of the fundamental group of the surface π1(S), we associate to any cut d a weight wϵ(d)∈Z2g+b, where g is the genus of S and b the number of boundary components. The main result of the paper asserts that the derived equivalence class of the surface algebra is determined by the corresponding weight wϵ(d) up to homeomorphism of the surface. Surface algebras are gentle and of global dimension ≤2, and any surface algebras coming from the same surface (S,M) are cluster equivalent, in the sense of [2]. To prove that the weight is a derived invariant we strongly use results about cluster equivalent algebras from [2].
Furthermore we also show that for surface algebras the invariant defined for gentle algebras by Avella-Alaminos and Geiss in [6] is determined by the weight.