Induced maps in homology for p-toral compact Lie groups

For stable splittings of the classifying spaces of general p-toral compact Lie groups, it is important step to describe the induced maps of the stable maps on F_p-homology. In this paper, we give the structure of the induced maps on F_p-homology for the classifying spaces of p-toral compact Lie groups. For this purpose, we show that there exists a transfer map τ : BF_∞p^Λ → BH_∞p^Λ where F_∞ is a p-discrete toral group and H_∞ is a subgroup of F_∞, and we combine this result with the property that A_f(F_∞, K) is dense in slim_nA(F_n, K)_p^Λ.