Induced maps in homology for p-toral compact Lie groups

Abstract

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 tau: BFinfinity pboolean AND --> BHinfinity pboolean AND where F-infinity is p-discrete toral group and H-infinity is a subgroup of F, and we combine this result with the property that A(f)(F-infinity, K) is dense in <(lim)under left arrow>(n)A(F-n, K)(p)(boolean AND). (C) 1998 Elsevier Science B.V.