Homotopy normality of Lie groups and the adjoint action (Q1890297)

The authors study the homotopy normality of some homomorphisms of Lie groups, as defined by \textit{I. James} [An. Acad. Brasil. Ciens. 39, 39--44 (1967; Zbl 0156.21603)] and \textit{G. S. McCarthy} [Q. J. Math., Oxf. II. Ser. 15, 362-370 (1964; Zbl 0123.16102)]. They use the adjoint action on the space of based loops and prove several results as for example: Let \(f\colon H\to G\) be a homomorphism of Lie groups where \(H\) is compact and connected, \(\pi_1(H)_{(3)}=0\), \(G=F_4\), \(E_6\) or \(E_7\). If \({\mathcal P}^1f^*H^3(G)\neq 0\), if \(H_*(H;{\mathbb Z})\) is 3-torsion free and if \(QH^{23}(H;{\mathbb Q})=0\), then \(f\) is not mod 3 homotopy normal.