Modular coinvariants and the mod p homology of QS^k

Abstract

We use modular invariant theory to establish a complete set of relations of the mod $p$ homology of $\{Q{S}^k{\}}_{k\ge 0}$, for $p$ odd, as a ring object in the category of coalgebras (also known as a coalgebraic ring or a Hopf ring). We also describe the action of the mod $p$ Dyer-Lashof algebra as well as the mod $p$ Steenrod algebra on the coalgebraic ring.

26 pages; To appear in Proceedings of the London Mathematical Society

References in corpus (1)

• Adem relations in the Dyer-Lashof algebra and modular invariants