On spaces of functions between classifying spaces
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 \(BG\to BL\).
homotopy type of the space of maps between classifying spaces
scientific article; zbMATH DE number 78192