Quasifolds

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.