On the monodromy of KZ-connections with irregular singularities

TL;DR

This paper investigates the monodromy of KZ-connections with irregular singularities, providing general results and explicit examples of link invariants derived from monodromy in configuration spaces.

Contribution

It offers new insights into the monodromy of KZ-connections with higher-order poles and connects these to topological invariants of links and tangles.

Findings

General results on monodromies of irregular KZ-connections

Explicit examples of link invariants from monodromy

Analysis of both universal and Lie algebra-specific cases

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.