Subject: Polyhedral sets
Date: Tue, 23 Apr 2002 08:00:36 +0100
From: "Ronald Brown"
To: "Don Davis"
reply to r.brown@bangor.ac.uk
A general theory of polyhedral sets appeared in D.W.Jones, Polyhedral
$T$-complexes, University of Wales PhD Thesis, 1984; published as A general
theory of polyhedral sets and their corresponding $T$-complexes, Diss. Math.
266, 1988.
In order to be able to do Kan filling constructions, this uses a notion of
shellability from combinatorics. Part of the interest is that orientation is
generalised to a notion of marked faces, so that for example a triangle can
have any directions on the edges. This also allows homotopy rather than
homology type constructions.
It is directed towards groupoids rather than categories and so it would be
interesting to compare this with work of Steiner on directed complexes.
Copies are available from the publishers of Diss. Math.
Ronnie Brown
> Subject: more
> Date: Fri, 19 Apr 2002 13:31:37 -0400
> From: jim stasheff
>
> My memory - oy!
> Saneblidze and Kadeishvili cite
> Saneblidze and Umble where permutahedral sets first appear.
>
>
>