Subject: Re: 2 questions Date: Tue, 29 Apr 2003 15:23:43 -0500 From: Brayton Gray To: Don Davis CC: Brayton Gray for the list: A long time ago Sugawara proved that if T is a connected H space of the homotopy type of a CW complex, thee is a fibering of the form: T -----> T*T ------>ST Where the projection is the Hopf construction on the multiplication. Continuing the fiber sequence to the left, we have a map: LST ----> T Where LST is the loop space of the suspension of T. Presumably this is an extension of the multiplication: T x T ----> LST ----> T Does anyone know of a reference for this or a proof? Since there are other maps T x T ----> T for connected CW H spaces involving inverse maps, it is conceivable that this presumption is false.