Equivariant stable stems for prime order groups

TL;DR

This paper studies equivariant stable maps for prime order groups using Borel cohomology and spectral sequences, revealing how stability, duality, and dimension functions influence the equivariant stable homotopy category.

Contribution

It extends the understanding of equivariant stable maps by analyzing their structure via spectral sequences and module categories, highlighting the role of dimension functions.

Findings

Equivariant stable maps are characterized using Borel cohomology Adams spectral sequence.

Stability and duality properties lift to module categories over Steenrod algebra.

Dependence of the structure on the dimension functions of representations is clarified.

Abstract

For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and duality, are shown to lift to the category of modules over the associated Steenrod algebra. The dependence on the dimension functions of the representations is clarified.