We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.

‎In this paper‎, ‎we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${mathcal{A}_p}^*$ under the conjugation map $chi$ and give bounds on the dimensions of $(chi-1)({mathcal{A}_p}^*)_d$‎, ‎where $({mathcal{A}_p}^*)_d$ is the dimension of ${mathcal{A}_p}^*$ in degree $d$‎.

We discuss which transition matrices between some pairs of additive bases the mod p Steenrod algebra with Bockstein element are triangular.

We describe a minimal unstable module presentation over the Steenrod algebra for the odd-primary cohomology of infinitedimensional complex projective space and apply it to obtain a minimal algebra presentation for the cohomology of the classifying space of the infinite unitary group. We also show that there is a unique Steenrod module structure on any unstable cyclic module that has dimension o...

In this paper we study the relationships between operations in K-theory and ordinary mod p cohomology. In particular, conditions are given under which the mod p associated graded ring of a filtered λ-ring is an unstable algebra over the Steenrod algebra. This result partially extends to the algebraic setting a topological result of Atiyah about operations on K-theory and mod p cohomology for to...

While all of the relations in the Steenrod algebra, A, can be deduced in principle from the Adem relations, in practice, it is extremely difficult to determine whether a given polynomial of elements in A is zero for all but the most elementary cases. In his original paper [Mi] Milnor states “It would be interesting to discover a complete set of relations between the given generators of A”. In p...

Fix a prime p, and let A be the polynomial part of the dual Steenrod algebra. The Frobenius map on A induces the Steenrod operation P̃0 on cohomology, and in this paper, we investigate this operation. We point out that if p = 2, then for any element in the cohomology of A, if one applies P̃0 enough times, the resulting element is nilpotent. We conjecture that the same is true at odd primes, and t...