Subject: Re: three postings
From: jim stasheff <jds@math.upenn.edu>
Date: Sun, 05 Aug 2007 14:36:32 -0400

> homotopy commutative cube means only that the square faces commute up to 
homotopy?
then surely the lack of a `bulk' homotopy is the problem

given such a bulk homotopy, can we rectify?

jim


On Aug 5, 2007, at 12:55 PM, Don Davis wrote:

> From: Jeffrey Smith <jhs@math.ubc.ca>
>
> Date: Mon, 30 Jul 2007 00:10:16 -0700 (PDT)
>
>
> Hi:
>
>
> I believe that it is not possible to rectify every homotopy commutative 
cube as otherwise every triple Toda bracket would vanish mod 
indeterminacy.
>
>
> Jeff Smith
>
>
>
> On Fri, 27 Jul 2007, Don Davis wrote:
>
>
> > Subject: question about homotopy commutative diagram
>
> > From: Gaucher Philippe <gaucher@pps.jussieu.fr>
>
> > Date: Thu, 26 Jul 2007 19:18:54 +0200
>
> >
>
> > Dear all,
>
> >
>
> > I'd like to prove that it is possible to rectify a homotopy 
commutative cube
>
> > of topological spaces. I know how to do that using the Boardman-Vogt
>
> > construction but it's very complicated. Does anyone know a paper where 
this
>
> > fact is already proved ?
>
> >
>
> > Thanks in advance. pg.