Subject: loop group question From: John Baez Date: Sun, 29 Oct 2006 13:32:05 -0800 Dear Topologists - Does anyone know a reference for the fact that given a compact Lie group G, the usual based loop group {f: S1 -> G: f(*) = 1, f smooth} is homotopy equivalent to this slightly different one: {f: [0,1] -> G: f(0) = f(1) = 1, f smooth} ? The first is a proper subgroup of the second, since we demand smoothness at the basepoint *. Here I'm giving both these groups their C^infinity topology. I think I could prove this quickly if both these groups have the homotopy type of a CW complex. So, a reference for that would also make me happy. Best, jb