Quasispheres can be approximated by smooth spheres.
arXiv research
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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 identi…
We consider decomposition spaces that are manifold factors and admit defining sequences consisting of cubes-with-handles. Metrics on constructed via modular embeddings into Euclidean spaces promote the controlled topology to a controlled geometry. The quasisymmetric parametrizability of the metric spa…