A restriction for singularities on collapsing orbifolds

TL;DR

This paper proves a uniform bound on the size of local symmetry groups at singularities in collapsing orbifolds with isolated singularities, advancing understanding of their geometric structure.

Contribution

It establishes a new restriction on the size of local groups at singularities in collapsing orbifolds, which was previously unknown.

Findings

Bound on |G_x| for collapsing orbifolds with isolated singularities

Uniform control over local symmetry groups

Insight into the structure of singularities in collapsing orbifolds

Abstract

An orbifold $X$ is locally homeomorphic to $G_x\backslash B_r(0)$, where $G_x$ is a finite group acting on $B_r(0)\subset{\mathbb R}^n$, so that $G_x(0)=0$. For collapsing orbifolds with isolated singularities, we show there is a uniform bound in $|G_x|$.