## Spherical objects and simple curves

#### Sebastian Opper (Cologne)

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 $$Perf(E_n)$$.