Subject: RE: cofibrant G-space
Date: Tue, 12 Aug 2003 19:31:51 +0100
From: "Neil Strickland"
To: "Don Davis"
If I remember rightly
(1) Most of Strom's work reduces to constructions with neighbourhood
deformation retracts, and with the data that prove that a subspace
has the NDR property.
(2) All his constructions are so canonical that they can immediately
be made equivariant.
(3) At least part of this programme was carried out by Peter May and/or
his collaborators, with emphasis on the symmetric groups. They
needed it to prove that certain operadic bar constructions etc had
reasonable homotopical properties. I think that some of this work,
or at least a reference to it, may be in the book "E_\infty ring
spaces and E_\infty ring spectra". But I am trying to remember
things that I have not looked at for a long time.
Neil
> >
> > Subject: cofibrant G-space
> > Date: Tue, 12 Aug 2003 11:46:18 +0200 (MEST)
> > From: Philippe Gaucher
> >
> > There exists on the category of topological spaces a model structure
> > where
> > the weak equivalences are the homotopy equivalences (Strom). In this
> > model
> > structure, all spaces are fibrant and cofibrant. I would be
> interesting
> > in
> > any reference concerning a similar model structure for G-spaces. And
> > particularly how cofibrant objects looks like ? Probably a cofibrant
> > G-space is a G-space with G acting freely in some sense on the space.
> >
> > pg.