A note on the equivariant Dold–Thom theorem

✍ Scribed by Pedro F. dos Santos

• Book ID: 104152655
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 203 KB
• Volume: 183
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(03)00029-x

✦ Synopsis

In this note we prove a version of the classical Dold-Thom theorem for the RO(G)-graded equivariant homology functors H G * (-; M ), where G is a ÿnite group, M is a discrete Z[G]-module, and M is the Mackey functor associated to M . In the case where M =Z with the trivial G-action, our result says that, for a G-CW-complex X , and for a ÿnite dimensional G-representation V, there is a natural isomorphism

where Z0(X ) denotes the free abelian group on X .