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Computation of categorical entropy via spherical functors
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abstract
We study the relationship between the categorical entropy of the twist and cotwist functors along a spherical functor. In particular, we prove the categorical entropy of the twist functor coincides with that of the cotwist functor if the essential image of the right adjoint functor of the spherical functor contains a split-generator. We also see our results generalize the computations of the categorical entropy of spherical twists and $\mathbb{P}$-twists by Ouchi and Fan. As an application, we apply our results to the Gromov--Yomdin type conjecture by Kikuta--Takahashi.
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Cited by 1 Pith paper
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Statistical Mechanics and Categorical Entropy
The paper claims algebraic integrality of lattice entropy growth, but the proof has a critical gap, and the categorical entropy link is left as a conjecture.
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