The Bredon-Löffler conjecture

J. P. C. Greenlees R. R. Bruner

Abstract

We give a brief exposition of results of Bredon and others on passage to fixed points from stable C_{2} equivariant homotopy and its relation to Mahowald’s root invariant. In particular we give Bredon’s easy equivariant proof that the root invariant doubles the stem; the conjecture of the title is equivalent to the Mahowald-Ravenel conjecture that the root invariant never more than triples the stem. Our main result is to verify by computation that the algebraic analogue of this holds in an extensive range.