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equivariant triangulation theorem

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

The equivariant triangulation theorem (Illman 78, Illman 83) says that for GG a compact Lie group (for instance a finite group) and XX a compact smooth manifold equipped with a smooth GG-action, there exists a GG-equivariant triangulation of XX.

(Illman 83, theorem 7.1, corollary 7.2) Recalled as (ALR 07, theorem 3.2). See also Waner 80, p. 6 who attributes this to Matumoto 71

Moreover, if the manifold does have a boundary, then its G-CW complex may be chosen such that the boundary is a G-subcomplex. (Illman 83, last sentence above theorem 7.1)

Applications

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)

See also

  • T. Matumoto, Equivariant K-theory and Fredholm operators, J. Fac. Sci. Tokyo 18 (1971/72), 109-112 (jairo)

  • Stefan Waner, Equivariant Homotopy Theory and Milnor’s Theorem, Transactions of the American Mathematical Society Vol. 258, No. 2 (Apr., 1980), pp. 351-368 (JSTOR)

  • A. Adem, J. Leida and Y. Ruan, Orbifolds and Stringy Topology, Cambridge Tracts in Mathematics 171 (2007) (pdf)

Created on February 19, 2019 at 04:33:37. See the history of this page for a list of all contributions to it.