A theorem by Burban and Drozd (2011) states that the category Perf En of perfect complexes over a cycle of projective lines \(E_n\) \((n\in N)\) can be modeled by a subcategory of \(D^b(\Gamma_n)\), the bounded derived category of finitely generated modules over a certain gentle algebra \(\Gamma_n\). In particular, questions about spherical objects in \(Perf(E_n)\) and their associated spherical twists can be studied by means of the gentle algebra. Inspired by the Homological Mirror Symmetry Conjecture, I will establish a connection between homotopy bands of \(\Gamma_n\) in the sense of Bekkert and Merklen (2003) and certain curves on the torus with \(n\) punctures. I will explain how the combinatorics of morphisms, mapping cones and spherical twists in \(D^b(\Gamma_n)\) are connected to intersection points, surgeries and Dehn twists by simple curves. Finally, I will talk about applications to spherical objects in \(Perf(E_n)\).