  Homological mirror symmetry predicts that there is a relation between
autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau
varieties, and the symplectic mapping class groups of symplectic manifolds. In
this paper, as an analogue of Dehn twists for mapping class groups of closed
oriented real surfaces, we study spherical twists for derived categories of
algebraic varieties. We introduce the intersection number and relate it to
group-theoretic properties of spherical twists. As an application, we compute
the center of autoequivalence groups of derived categories of K3 surfaces.
