# The Reidemeister spectrum of low dimensional almost-crystallographic groups

## TL;DR

This paper investigates the Reidemeister spectrum of low-dimensional almost-crystallographic groups, identifying those with the $R_
Infty$-property and computing spectra for specific 3- and 4-dimensional groups.

## Contribution

It provides a classification of 4-dimensional almost-crystallographic groups with the $R_
Infty$-property and calculates Reidemeister spectra for certain low-dimensional groups.

## Key findings

- Identified which 4D almost-crystallographic groups have the $R_
Infty$-property.
- Computed Reidemeister spectra for 3D almost-crystallographic groups.
- Calculated spectra for 4D almost-Bieberbach groups.

## Abstract

We determine which non-crystallographic, almost-crystallographic groups of dimension 4 have the $R_\infty$-property. We then calculate the Reidemeister spectra of the 3-dimensional almost-crystallographic groups and the 4-dimensional almost-Bieberbach groups.