Invariants of tangles with flat connections in their complements.I. Invariants and holonomy R-matrices

TL;DR

This paper introduces holonomy R-matrices and demonstrates how to define invariants of tangles with flat connections in their complements using these matrices, advancing the understanding of topological invariants in the context of flat G-bundles.

Contribution

It introduces the concept of holonomy R-matrices and shows how to construct invariants of tangles with flat connections in their complements.

Findings

Holonomy R-matrices are defined.

Invariants of tangles with flat connections are constructed.

The approach links flat G-bundles with topological invariants.

Abstract

The notion of holonomy $R$-matrices is introduced. It is shown how to define invariants of tangles with flat connections in a principle $G$-bundle of the complement of a tangle using holonomy $R$-matrices.