Talk:Classifying space for U(n)

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For the case N=1,it is incorrect to say EU(1) = CP^\infty. This is not contractible,for one thing, and contradicts what is said above about the general case, where EU(n) is the set of orthonormal N-frames in Hilbert space. So for N=1, this reduces to the case of the unit sphere in Hilbert space - which is contractible - see e.g. http://www.math.ucr.edu/home/baez/week151.html Cgwaldman 06:23, 29 September 2007 (UTC)

I removed the stuff that ES^1 is a unit sphere in Hilbert space (kinda projective limit of finite-dim spaces), instead inserting CP^\infty (inductive limit). 18.87.0.72 04:02, 31 October 2005 (UTC)

Seems like the same thing to me, isn't it? linas 07:04, 1 November 2005 (UTC)

Not at all. The only complex projective space that is ismorphic to a shpere is CP(1). If I remember well, the unit sphere in a Hilbert space is contractible (please correct me if I'm wrong or write a reference if you know one) whereas has its cohomology isomorphic to . S.racaniere 23:47, 30 December 2006 (UTC)