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arXiv · 2312.14905

Unlinking symmetric quivers

Piotr Kucharski·Hélder Larraguível·Dmitry Noshchenko·Piotr Sułkowski
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Abstract

We analyse the structure of equivalence classes of symmetric quivers whose generating series are equal. We consider such classes constructed using the basic operation of unlinking, which increases a size of a quiver. The existence and features of such classes do not depend on a particular quiver but follow from the properties of unlinking. We show that such classes include sets of quivers assembled into permutohedra, and all quivers in a given class are determined by one quiver of the largest size, which we call a universal quiver. These findings generalise the previous ones for permutohedra graphs for knots. We illustrate our results with generic examples, as well as specialisations related to the knots-quivers correspondence.

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Piotr Kucharski, Hélder Larraguível, Dmitry Noshchenko, Piotr Sułkowski. 2023-12-22. Unlinking symmetric quivers. https://arxiv.org/abs/2312.14905

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