A restriction for singularities on collapsing orbifolds

2011/01/24 by Yu Ding, Ding, Yu
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1101.4444

Preprint. 9 pages. The bound for $|G_x|$ is corrected to $(2π/0.47)^{n(n-1)}$

arxiv created 2011/07/07 · arxiv updated 2011/07/08

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)⊂\mathbb Rⁿ, so that G_x(0)=0. For collapsing orbifolds with isolated singularities, we show there is a uniform bound in |G_x|.

Related

• Obstructions to smoothing orbicurves and Orbifold Hecke algebras
• A general collapsing result for families of stratified Riemannian metrics on orbifolds
• Orbifolds and manifold quotients with upper curvature bounds
• Orbifold equivalence: structure and new examples
• Orbifold Quotients of Symmetric Domains of Tube type