English

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 WW is a piecewise Euclidean CAT(0) space on which WW acts properly, cocompactly by isometries. The one skeleton of the Davis complex can be identified with the Cayley graph of WW. 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}
}
R2 v1 2026-06-22T19:46:08.295Z