Groups of unstable Adams operations on \(p\)-local compact groups (Q507055)

Let \(G\) be a compact connected Lie Group. An unstable Adams operation of degree \(k \geq 1\) on \(BG\) is a self map \(f: BG \;\rightarrow \;BG\) which induces multiplication by \(k^{i}\) on \(H^{2i}(BG; {\mathbb Q})\) for every \(i > 0\). \textit{F. Junod} et al. [Algebr. Geom. Topol. 12, No. 1, 49--74 (2012; Zbl 1258.55010)] defined unstable Adams operations on \(p\)-local compact groups in two ways. One relies only on the algebraic structure of the \(p\)-local compact group. This definition the authors of the paper reviewed here call algebraic. The second definition which the authors call geometric is more closely related to the way that unstable Adams operations are defined for compact Lie and \(p\)-compact groups. This paper gives a description of the relationship between the group of geometric and the group of algebraic unstable Adams operations. The authors show that under some conditions unstable Adams operations are determined by their degree.