Two more responses re delta sets, etc.....DMD
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Subject: Re: facial sets
Date: Fri, 04 Feb 2000 10:11:12 -0100
From: "Carlos.SIMPSON" <carlos@math.unice.fr>

  Since noone seems to have found an already-existing standard
(the terminology ``Delta set'' suffers from the fact that the standard notation
for the usual simplicial category (with degeneracies) is $\Delta$),
here is a suggestion: ``facial sets''. This is somewhat like ``face complex''
but could apply to other objects eg ``facial groups'' etc...
---Carlos Simpson
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Date: Thu, 3 Feb 2000 14:34:07 -0500 (EST)
From: James Stasheff <jds@math.unc.edu>
Subject: Re: response re delta sets

what about the distinction between the fat realization and the thin??

.oooO   Jim Stasheff            jds@math.unc.edu
(UNC)   Math-UNC                (919)-962-9607
 \ (    Chapel Hill NC          FAX:(919)-962-2568
  \*)   27599-3250

        http://www.math.unc.edu/Faculty/jds

On Thu, 3 Feb 2000, DON DAVIS wrote:

> From: Jeff Smith <jhs@math.purdue.edu>
> Subject: Re: delta sets
> Date: Thu, 3 Feb 2000 14:10:20 -0500 (EST)
>
> >
> > Date: Fri, 28 Jan 2000 14:50:49 -0500 (EST)
> > From: Allen Hatcher - Math Prof <hatcher@math.cornell.edu>
>
> > Subject: Delta set terminology
> >
> >      Here's a comment for the discussion list:
> >
> > Concerning the Delta set terminology: A related issue is what to call the
> > geometric incarnations of Delta sets. These are CW complexes with special
> > structure. In Brayton Gray's book they are called "semisimplicial CW
> > complexes." Does anyone know of other names in the literature?
> >
> > These geometric objects occur rather often in the algebraic topology
> > textbook I'm writing, so I wanted a shorter name and chose to call them
> > "Delta complexes" since they are somewhere between simplicial complexes
> > and CW complexes, and they are logically the same as Rourke and
> > Sanderson's Delta sets. I hope the new terminology doesn't muddy the
> > waters too much. In any event, the geometric concept seems extremely
> > useful as well as natural, so it deserves to have its own name, and this
> > is my candidate.
> >
> > Allen Hatcher
> >
>
>
> One comment,  the CW-complexes that arise as the geometric realization of a
> Delta set are the same CW-complexes that arise as the geometric realization
> of a simplicial set.  In fact there is a functor sending the the Delta set
> X to the simplicial set sX such that the geometric realization of the Delta
> set X is the same CW-complex as the geometric realization of the siplicial set
> sX.
>
> Geometrically there is no difference between Delta sets and
> simplicial sets.
>
>
> Jeff Smith
>
>
>