A dual Rothenberg-Steenrod spectral sequence

Invariant elements in the dual Steenrod algebra

‎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 $d$‎.

Algebraic Steenrod Operations in the Spectral Sequence Associated W I T H a Pair of Hopf Algebras

Some Quotient Hopf Algebras of the Dual Steenrod Algebra

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...

Steenrod coalgebras

Article history: Received 4 December 2013 Received in revised form 23 February 2015 Accepted 24 February 2015 Available online 5 March 2015

A spectral sequence for splines

We de ne a complex R=J of graded modules on a d-dimensional simplicial complex , so that the top homology module of this complex consists of piecewise polynomial functions (splines) of smoothness r on the cone of . In a series of papers ([4], [5], [6]), Billera and Rose used a similar approach to study the dimension of the spaces of splines on , but with a complex substantially di erent fromR=J...