BP-homology of elementary abelian 2-groups: BP-module structure

TL;DR

This paper analyzes the BP-homology of elementary abelian 2-groups, revealing its module structure over BP and connecting it to symmetric polynomials and Dickson invariants.

Contribution

It determines the BP-module structure of the main part of the BP-homology for elementary abelian 2-groups, advancing understanding of their algebraic topology.

Findings

BP-module structure characterized

Connection to symmetric polynomials established

Relation to Dickson invariants identified

Abstract

We determine the BP-module structure, mod higher filtration, of the main part of the BP-homology of elementary abelian 2-groups. The action is related to symmetric polynomials and to Dickson invariants.