## Experimental Mathematics

- Experiment. Math.
- Volume 4, Issue 4 (1995), 289-297.

### The Bredon-Löffler conjecture

Robert Bruner and John Greenlees

#### Abstract

We give a brief exposition of results of Bredon and others on passage to fixed points from stable $C_2$ equivariant homotopy (where $C_2$ is the group of order two) 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: this improves on results of [Mahowald and Shick 1983].

#### Article information

**Source**

Experiment. Math., Volume 4, Issue 4 (1995), 289-297.

**Dates**

First available in Project Euclid: 14 March 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1047674389

**Mathematical Reviews number (MathSciNet)**

MR1387694

**Zentralblatt MATH identifier**

0858.55012

**Subjects**

Primary: 55Q45: Stable homotopy of spheres

Secondary: 55Q10: Stable homotopy groups 55Q91: Equivariant homotopy groups [See also 19L47] 55S10: Steenrod algebra 55T15: Adams spectral sequences

#### Citation

Bruner, Robert; Greenlees, John. The Bredon-Löffler conjecture. Experiment. Math. 4 (1995), no. 4, 289--297. https://projecteuclid.org/euclid.em/1047674389