A subanalytic triangulation theorem for real analytic orbifolds

TL;DR

This paper proves that real analytic orbifolds can be uniquely triangulated compatibly with their strata, and extends the triangulation results to differentiable orbifolds, generalizing previous quotient orbifold theorems.

Contribution

It establishes a unique subanalytic triangulation for real analytic orbifolds and shows that every ${ m C}^r$-orbifold admits a real analytic structure, enabling triangulation of differentiable orbifolds.

Findings

Unique subanalytic triangulation compatible with strata

Extension of triangulation to ${ m C}^r$-orbifolds

Generalization of previous quotient orbifold results

Abstract

Let $X$ be a real analytic orbifold. Then each stratum of $X$ is a subanalytic subset of $X$. We show that $X$ has a unique subanalytic triangulation compatible with the strata of $X$. We also show that every ${\rm C}^r$-orbifold, $1\leq r\leq \infty$, has a real analytic structure. This allows us to triangulate differentiable orbifolds. The results generalize the subanalytic triangulation theorems previously known for quotient orbifolds.