Nilpotence and torsion in the cohomology of the Steenrod algebra

Abstract

In this paper we prove the existence of global nilpotence and global torsion bounds for the cohomology of any finite Hopf subalgebra of the Steenrod algebra for the prime 2 2 . An explicit formula for computing such bounds is then obtained. This is used to compute bounds for H ∗ ( A n ) {H^{\ast } }({\mathcal {A}_n}) for n ≤ 6 n \leq 6 .