On spaces of functions between classifying spaces (Q1196323)

The paper under review extends the results of \textit{W. Dwyer} and the author [Algebraic topology, Proc. Symp., Barcelona/Spain 1986, Lect. Notes Math. 1298, 106-119 (1987; Zbl 0646.55007)]. The main result: Let \(L\) be a compact Lie group and \(G\) either a \(p\)- group or a torus. Then every map \(f: GB\to BL\) between the classifying spaces is homotopic to a map \(B\varphi\), where \(\varphi\) is a homomorphism \(G\to L\). If \(\varphi_ 0,\varphi_ 1: G\to L\) are two homomorphisms, then \(B\varphi_ 0\) is homotopic to \(B\varphi_ 1\) iff there is an inner automorphism \(\alpha\) of \(L\) such that \(\varphi_ 1=\alpha\varphi_ 0\). From this result the author deduces some results on the homotopy type of the space of maps \(BG\to BL\).