Topological Abelian Groups and Equivariant Homology

Abstract

We prove an equivariant version of the Dold–Thom theorem by giving an explicit isomorphism between Bredon–Illman homology and equivariant homotopical homology π_*(F ^G (X, L)), where G is a finite group and L is a G-module. We use the homotopical definition to obtain several properties of this theory and we do some calculations.

Key Words:

• Coefficient systems
• Equivariant homology
• Equivariant homotopy

2000 Mathematics Subject Classification:

• 55N91
• 55P91
• 14F43

ACKNOWLEDGMENT

Carlos Prieto was partially supported by PAPIIT grant IN110902 and by CONACYT grant 43724.

Notes

¹Notice that the system of invariants of L is denoted by L in Lima-Filho (1997) and dos Santos (2003).

Communicated by R. H. Villarreal.