# The Alexander polynomial for closed braids in lens spaces

## TL;DR

This paper introduces a new method to compute the Alexander polynomial of links in lens spaces using a Burau-like representation of the mixed braid group, simplifying calculations in this setting.

## Contribution

It develops a reduced Burau-like representation for the mixed braid group in lens spaces and enables direct calculation of the Alexander polynomial from mixed braids.

## Key findings

- Provides a new algebraic tool for link invariants in lens spaces
- Enables direct computation of Alexander polynomial from mixed braids
- Simplifies previous methods for analyzing links in lens spaces

## Abstract

We present a reduced Burau-like representation for the mixed braid group on one strand representing links in lens spaces and show how to calculate the Alexander polynomial of a link directly from the mixed braid.