Subject: Re: four postings From: "D. Notbohm" Date: Mon, 5 Dec 2005 11:37:13 +0000 (GMT) Let P be a p-toral group, i.e. an extension of a torus by a finite p-group. and $G$ a compact Lie group. Then, every map BP -->BG is induced by a continuous homomorphism P-->G. I proved this in my paper "Maps between classifying spaces, Math. Z. 207, (1991), 153-168. Unfortunately, the main theorem does not contain the word continuous, but that is what I had in mind. There also exist a proof by Zabrodsky, Israel J. (1991). Dietrich Notbohm >>Subject: question for the list >>From: Tom Goodwillie >>Date: Fri, 2 Dec 2005 10:25:11 -0500 >> >>Recent questions about BSU(n) made me think of the following question, >>which I am sure someone can answer: >> >>If T is a product of circle groups and G is a compact Lie group, then >>does every homotopy class >> >>BT --> BG >> >>arise from a continuous homomorphism T --> G ? >> >>In particular, is every complex vector bundle on BU(1), or on a product >>of copies of BU(1), a direct sum of line bundles? >> >> Tom Goodwillie >>____________________________________________________________