Subject: Re: four postings From: Clarence W Wilkerson Jr Date: Mon, 28 Nov 2005 12:26:18 -0500 BU(n) and BSU(n) x BS1 are not homotopy equivalent at the prime $p=2$, but are at other primes. The mod 2 Steenrod algebra should detect the non-equivalence. In particular, I suspect that Sq2 behaves differently on the two spaces. Clarence > > Subject: Some questions > From: Johannes Ebert > Date: Thu, 24 Nov 2005 18:07:49 +0100 (CET) > > I have several questions. First: Consider the groups U_n and SU_n \times U_1. > They are diffeomorphic, but not isomorphic as groups. What about the classifying > spaces BSU_n \times U_1 and BU_n? Are they homotopy equivalent ot not? I think > they are not homotopy equivalent, but I do not know a proof. >