Categorical vs topological entropy of autoequivalences of surfaces

Abstract

In this paper, we give an example of an autoequivalence with positive categorical entropy (in the sense of Dimitrov, Haiden, Katzarkov and Kontsevich) for any surface containing a (-2)-curve. Then we show that this equivalence gives another counter-example to a conjecture proposed by Kikuta and Takahashi. In a second part, we study the action on cohomology induced by spherical twists composed with standard autoequivalences on a surface S and show that their spectral radii correspond to the topological entropy of the corresponding automorphisms of S.

v2: minor correction, published in the Moscow Mathematical Journal

References in corpus (3)

• Infinitesimal Derived Torelli Theorem for K3 surfaces
• Categorical entropy for Fourier-Mukai transforms on generic abelian surfaces
• On entropy of spherical twists

Cited by in corpus (4)

• Entropy of the composition of two spherical twists
• Hochschild entropy and Categorical entropy
• A comparison of categorical and topological entropies on Weinstein manifolds
• On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity