Chamber Complexes, Coxeter Systems, and Buildings

 Title: Chamber Complexes, Coxeter Systems, and Buildings Author: Jeremy Sylvestre Submission date: 2016-07-01 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}, } License: BSD License