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arXiv · 1909.02758

Categorical vs topological entropy of autoequivalences of surfaces

Dominique Mattei
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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.

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Dominique Mattei. 2019-09-06. Categorical vs topological entropy of autoequivalences of surfaces. https://doi.org/10.17323/1609-4514-2021-21-2-401-412

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