Entropy of an autoequivalence on Calabi-Yau manifolds

We prove that the categorical entropy of the autoequivalence T-O o (- circle times O (-1)) on a Calabi-Yau manifold of dimension d >= 3 is the unique positive real number lambda satisfying Sigma(k >= 1)chi(O(k))/e(k lambda) = e((d-1)t). We then use this result to construct the fi rst counterexamples of a conjecture on categorical entropy by Kikuta and Takahashi.