A localization theorem for equivariant connective K theory

TL;DR

This paper establishes a localization theorem for equivariant connective K-theory spectra associated with cyclic groups, connecting Greenlees' spectrum to the connective cover of equivariant complex K-theory.

Contribution

It identifies Greenlees' equivariant connective K theory spectrum as an $RO(C_n)$-graded localization of the connective cover of $KU_{C_n}$, providing a new structural understanding.

Findings

Greenlees' spectrum is an $RO(C_n)$-graded localization.

Connective cover of $KU_{C_n}$ is explicitly characterized.

The result applies to cyclic groups $C_n$.

Abstract

For a cyclic group $C_n$, we identify Greenlees' equivariant connective K theory spectrum $kU_{C_n}$ as an $RO(C_n)$-graded localization of the actual connective cover of $KU_{C_n}$.