Chamber Complexes, Coxeter Systems, and Buildings
نویسنده
چکیده
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.
منابع مشابه
Connectivity of chamber graphs of buildings and related complexes
Let ∆ be a finite building (or, more generally, a thick spherical and locally finite building). The chamber graph G(∆), whose edges are the pairs of adjacent chambers in ∆, is known to be q-regular for a certain number q = q(∆). Our main result is that G(∆) is q-connected in the sense of graph theory. Similar results are proved for the chamber graphs of Coxeter complexes and for order complexes...
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ورودعنوان ژورنال:
- Archive of Formal Proofs
دوره 2016 شماره
صفحات -
تاریخ انتشار 2016