On the splitting of mapping spaces between classifying spaces. I
If H is a simple Lie group of rank 1 and \(G_ 1\), \(G_ 2\) are compact, connected Lie groups with finite fundamental groups, it is proved that in both the free and based categories, the space of mappings from \(B(G_ 1\times G_ 2)\) to BH is weakly equivalent to the push out over BH (free) or wedge (based) of the mapping spaces of \(BG_ 1\) and \(BG_ 2\) into BH. One of the corollaries is that the set of homotopy classes of maps from the product of h copies of \(HP^{\infty}\) to k copies of \(HP^{\infty}\) is equivalent to the set of (k\(\times h)\)-matrices with entries equal to 0 or \((2r+1)^ 2\) for any \(r\in Z\). The proofs use many recent results in the literature, particularly work on the ``Sullivan conjecture'' associated with the names of Miller and Zabrodsky and also cohomology models of classifying spaces of connected Lie groups using locally finite groups due to Friedlander and Mislin.
compact, connected Lie groups with finite fundamental groups
classifying spaces of connected Lie groups
scientific article; zbMATH DE number 4030505