The equivariant Dold theorem mod $k$ and the Adams conjecture

Abstract

In this paper, we state and prove a $G$-equivariant version of the Dold Theorem mod $k$ for finite groups $G$. We then use this theorem to prove an equivariant version of the Adams Conjecture for $G$ cyclic, using the Becker-Gottlieb approach. The case for general $G$ and finite structure groups is also obtained by the methods of Quillen.

We would like to express our gratitude to Professor J. P. May for his encouragement and many useful suggestions, and to the referee for his critical reading of the manuscript, and for his improvements on several of our proofs.