Quasifolds

TL;DR

This paper introduces quasifolds, a class of singular spaces generalizing manifolds and orbifolds, and illustrates their properties through a detailed example called the quasisphere.

Contribution

It defines quasifolds as spaces modeled by manifolds modulo countable group actions and provides a concrete two-dimensional example demonstrating their key features.

Findings

Quasifolds generalize manifolds and orbifolds.

The quasisphere exemplifies quasifold properties.

Quasifolds can be non-Hausdorff spaces.

Abstract

Quasifolds are singular spaces that generalize manifolds and orbifolds. They are locally modeled by manifolds modulo the smooth action of countable groups and they are typically not Hausdorff. If the countable groups happen to be all finite, then quasifolds are orbifolds and if they happen to be all equal to the identity, they are manifolds. In this article we illustrate quasifolds by describing a two-dimensional example that displays all of their main characteristics: the quasisphere.