A note on mapping class group actions on derived categories

Let Xnbe a cycle of n projective lines and Tn a symplectic torus with n punctures. Using the theory of spherical twists introduced by Seidel and Thomas, the author will define an action of the pure mapping class group of Tn on Db(Coh(Xn)). The motivation comes from homological mirror symmetry for degenerate elliptic curves, which was studied by the author with Treumann and Zaslow.