# Connective Bieberbach groups

## TL;DR

This paper characterizes connective Bieberbach groups, showing that those with trivial center are not connective and establishing that connective Bieberbach groups are precisely the poly-Z ones.

## Contribution

It provides a new criterion for connectivity in Bieberbach groups, linking it to the poly-Z property and the triviality of the center.

## Key findings

- Bieberbach groups with trivial center are not connective.
- A Bieberbach group is connective if and only if it is poly-Z.

## Abstract

We prove that a Bieberbach group with trivial center is not connective and use this property to show that a Bieberbach group is connective if and only if it is poly-Z.