Equivariant connective \(K\)-theory for compact Lie groups.
This paper gives a construction of a \(G\)-spectrum \(ku\), for \(G\) a compact Lie group, which is a \(G\)-equivariant analog of connective \(K\)-theory. It is a complex oriented, ring valued theory from which Atiyah-Segal equivariant \(K\)-theory can be obtained by inverting the Bott class and for which completion with respect to the augmentation ideal yields non-equivariant connective \(K\)-theory. Partial results are given concerning the coefficient ring \(ku_*^G\). For non-negative degrees, these agree with those of periodic \(K\)-theory and for degrees above \(-6\) they are described in terms of \(R(G)\). It is also shown that \(ku^G_{-6}\) can contain torsion.
scientific article; zbMATH DE number 2035897