Asymptotic shifting numbers in triangulated categories
Algebraic Geometry
2020-09-03 v2 Category Theory
Dynamical Systems
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.
Cite
@article{arxiv.2008.06159,
title = {Asymptotic shifting numbers in triangulated categories},
author = {Yu-Wei Fan and Simion Filip},
journal= {arXiv preprint arXiv:2008.06159},
year = {2020}
}
Comments
43 pages, 1 figure