Abstract: |
We provide a basic formal framework for the theory of chamber
complexes and Coxeter systems, and for buildings as thick chamber
complexes endowed with a system of apartments. Along the way, we
develop some of the general theory of abstract simplicial complexes
and of groups (relying on the group_add class for the basics),
including free groups and group presentations, and their universal
properties. The main results verified are that the deletion condition
is both necessary and sufficient for a group with a set of generators
of order two to be a Coxeter system, and that the apartments in a
(thick) building are all uniformly Coxeter. |
BibTeX: |
@article{Buildings-AFP,
author = {Jeremy Sylvestre},
title = {Chamber Complexes, Coxeter Systems, and Buildings},
journal = {Archive of Formal Proofs},
month = jul,
year = 2016,
note = {\url{http://isa-afp.org/entries/Buildings.html},
Formal proof development},
ISSN = {2150-914x},
}
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