Title:
On Conjugation Invariants in the dual Steenrod algebra
Authors:
M. D. Crossley and Sarah Whitehouse
AMS Classification Numbers:
55S10, 20J06, 20C30
Addresses:
Max-Planck-Institut fur Mathematik,
P.O. Box 7280,
D-53072 Bonn,
Germany.
Departement de Mathematiques,
Universite d'Artois - Pole de Lens,
Rue Jean Souvraz,
S. P. 18 - 63207 Lens,
France.
Email addresses:
crossley\@member.ams.org
whitehouse\@poincare.univ-artois.fr
Abstract Text:
We investigate the canonical conjugation chi of the mod 2 dual Steenrod algebra with a view to determining the subspace of elements invariant under chi. We give bounds on the dimension of this subspace for each degree and show that, after inverting xi_1, it becomes polynomial on a natural set of generators. Finally we note that, without inverting this class, the invariant subspace is far from being polynomial.
Note: This is a revised version of the paper of the same name we submitted last April. The only significant change is in section 5 where we withdraw a somewhat over-optimistic conjecture and correct some of the proofs.