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arXiv · 2603.24098

On the monodromy of KZ-connections with irregular singularities

Xia Gu·Babak Haghighat·Pavel Putrov
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Abstract

We study Knizhnik-Zamolodchikov (KZ) connection in the presence of irregular singularities, that is, poles of higher order. We consider both the case of a universal connection and the case when it is associated with a specific simple Lie algebra, such as $\mathfrak{su}(2)$. We give some general results about the monodromies of such flat connections in the configuration spaces of points, and provide explicit examples of topological invariants of links (more generally, tangles) realized by the monodromy.

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Xia Gu, Babak Haghighat, Pavel Putrov. 2026-03-25. On the monodromy of KZ-connections with irregular singularities. https://arxiv.org/abs/2603.24098

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