A note on mapping class group actions on derived categories

Abstract

Let X n X_n be a cycle of n n projective lines and T n \mathbb {T}_n a symplectic torus with n 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 T n \mathbb {T}_n on D b ( C o h ( X n ) ) D^b(Coh(X_n)) . The motivation comes from homological mirror symmetry for degenerate elliptic curves, which was studied by the author with Treumann and Zaslow.