The connective K-theory of the Eilenberg-MacLane space K(Z/p,2)

TL;DR

This paper computes the connective KU-cohomology and homology groups of the mod-p Eilenberg-MacLane space K(Z/p,2) using the Adams spectral sequence, revealing complex extension interactions.

Contribution

It provides the first detailed computation of ku^*(K(Z/p,2)) and ku_*(K(Z/p,2)), highlighting novel extension phenomena in the process.

Findings

Identification of h_0-extensions and exotic extensions

Determination of higher differentials in the spectral sequence

Explicit computation of connective KU (co)homology groups

Abstract

We compute ku^*(K(Z/p,2)) and ku_*(K(Z/p,2)), the connective KU-cohomology and connective KU-homology groups of the mod-p Eilenberg-MacLane space K(Z/p,2), using the Adams spectral sequence. We obtain a striking interaction between h_0-extensions and exotic extensions. The mod-p connective KU-cohomology groups, computed elsewhere, are needed in order to establish higher differentials and exotic extensions in the integral groups.