Visually-friendly manifolds with arbitrary finite fundamental group

TL;DR

This paper introduces a family of visually accessible manifolds that can realize any finite group as their fundamental group, providing a new way to visualize complex topological structures.

Contribution

The authors construct a family of metrizable, visually-friendly manifolds capable of exhibiting any finite fundamental group, expanding the toolkit for topological visualization.

Findings

Existence of manifolds with any finite fundamental group

Manifolds are metrizable and visually accessible

New examples of spaces with arbitrary finite fundamental groups

Abstract

We exhibit a family of metrizable manifolds such that any finite group appears as the fundamental group of one of them. These spaces are especially interesting as they can be easily visualized, as opposed to classical examples of spaces with arbitrary fundamental group.