nLab equivariant triangulation

Idea

For $X$ a manifold equipped with an action of a group $G$, a $G$-equivariant triangulation of $X$ is a triangulation of $X$ which is compatible with this $G$-action, in that this action restricts to bijections on sets of $k$-cells of the triangulation, for each $k \in \mathbb{N}$.

Properties

The equivariant triangulation theorem (Illman 78, Illman 83) asserts that for $G$ a compact Lie group (for instance a finite group) equivariant triangulations of smooth manifolds always exist.

Related concepts

• triangulation, triangulation theorem

• equivariant triangulation theorem

• equivariant differential topology

References

• Sören Illman, Smooth equivariant triangulations of $G$-manifolds for $G$ a finite group, Math. Ann. (1978) 233: 199 (doi:10.1007/BF01405351)

• Sören Illman, The Equivariant Triangulation Theorem for Actions of Compact Lie Groups, Mathematische Annalen (1983) Volume: 262, page 487-502 (dml:163720)