A subanalytic triangulation theorem for real analytic orbifolds

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 ${\mathrm{C}}^r$-orbifold, $1\le r\le \infty$, has a real analytic structure. This allows us to triangulate differentiable orbifolds. The results generalize the subanalytic triangulation theorems previously known for quotient orbifolds.

Made a minor change