# Augmentations and link group representations

## TL;DR

This paper introduces the augmentation representation, linking two different link invariants through a novel construction that associates fundamental group representations to augmentations of the framed cord algebra.

## Contribution

It presents a new method to connect link invariants by constructing the augmentation representation from the framed cord algebra augmentation.

## Key findings

- Establishes the augmentation representation as a bridge between link invariants.
- Analyzes properties of the augmentation representation.
- Connects algebraic and topological link invariants.

## Abstract

We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants of different types. We also study properties of the augmentation representation.