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.