Categorical vs topological entropy of autoequivalences of surfaces
arXiv:1909.02758 · doi:10.17323/1609-4514-2021-21-2-401-412
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.
arXiv commentv2: minor correction, published in the Moscow Mathematical Journal
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