nLab
equivariant triangulation

Contents

Context

Representation theory

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Idea

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

Properties

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

References

  • Sören Illman, Smooth equivariant triangulations of GG-manifolds for GG 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)

Created on February 19, 2019 at 04:39:51. See the history of this page for a list of all contributions to it.