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arXiv · 2008.06159

Asymptotic shifting numbers in triangulated categories

Yu-Wei Fan·Simion Filip
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Abstract

We introduce invariants, called shifting numbers, that measure the asymptotic amount by which an autoequivalence of a triangulated category translates inside the category. The invariants are analogous to Poincare translation numbers that are widely used in dynamical systems. We additionally establish that in some examples the shifting numbers provide a quasimorphism on the group of autoequivalences. Additionally, we relate our shifting numbers to the entropy function introduced by Dimitrov, Haiden, Katzarkov, and Kontsevich.

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Yu-Wei Fan, Simion Filip. 2020-08-14. Asymptotic shifting numbers in triangulated categories. https://arxiv.org/abs/2008.06159

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