Polyhedral T-complexes

[Ronnie Brown <ronnie.profbrown@btinternet.com>]

The notion of T-complex is discussed on the ncatlab which writes:

"A T-complex is a higher-dimensional combinatorial structure with a
class of designated thin elements. The concept can be made sense of for
various shapes:"

   (and then gives cubical and simplicial).

   I have put a link on that page
http://ncatlab.org/nlab/show/T-complex
to David Jones 1983 thesis `A general theory of polyhedral sets and the
corresponding T-complexes' which was kindly scanned recently by Stephen
Gaito. The theory there is for higher groupoids, and it is not clear how
to do higher categories in the same spirit.

The aims of this thesis were first to incorporate shapes like pentagons,
or other diagrams representing group relations, such as x^17=1,  then to
formulate multiple compositions,  and finally  to relate this theory to
that of simplicial T-complexes; but there are surely lots of other
issues worth pursuing further. I liked the  way the concept of
shellability is used in describing the basic `shapes', in order to give
power to the filling process.

While writing, I'll mention that pdf's of my seminar at Gottingen on May
5 on
`Applications of a nonabelian tensor product of groups'
are available on my preprint page:
http://www.bangor.ac.uk/r.brown/brownpr.html

Ronnie Brown



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