ON ENTROPY OF SPHERICAL TWISTS

In this paper, we compute categorical entropy of spherical twists. In particular, we prove that the Gromov-Yomdin-type conjecture holds for spherical twists. Moreover, we construct counterexamples of Gromov-Yomdin type conjecture for K3 surfaces modifying Fan's construction for even higher-dimensional Calabi-Yau manifolds. The appendix, by Arend Bayer, shows the nonemptiness of complements of a number of spherical objects in the derived categories of K3 surfaces.