Subject: Re: conf & question
Date: Tue, 12 Aug 2003 10:10:15 -0400 (EDT)
From: "John R. Klein"
To: Don Davis
The example of G-spaces is a special case of
a algebra over a triple (defined by the functor
X --> X x G).
If I remember correctly, Rainer Vogt (or maybe Vogt and Schwaezl)
proved a result which says that a alebras over a triple
(on spaces) form a model category. (I think this goes back to the
1970s.)
If one is willing to work with a Quillen type notion of weak equivalence:
X -> Y is a weak equivalence if it's a weak homotopy equivalence of
underlying spaces, then G-spaces can be equipped with a model structure
where the cofibrant spaces are retracts of free G-cellular spaces.
>
> 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.
>
>
>