Mapping the Davis complex into the imaginary cone
Group Theory
2017-05-16 v1
Abstract
The study of the set of limit roots associated to an infinite Coxeter group was initiated by Hohlweg, Labb\'{e} and Ripoll and further developed by Dyer, Hohlweg, P\'eaux and Ripoll. The Davis complex associated to a finitely generated Coxeter group is a piecewise Euclidean CAT(0) space on which acts properly, cocompactly by isometries. The one skeleton of the Davis complex can be identified with the Cayley graph of . In this paper we define a natural map from the Davis complex into the normalised imaginary cone of a based root system.
Keywords
Cite
@article{arxiv.1705.04837,
title = {Mapping the Davis complex into the imaginary cone},
author = {Xiang Fu and Lawrence Reeves},
journal= {arXiv preprint arXiv:1705.04837},
year = {2017}
}