Reflection subgroups of Coxeter groups

Abstract

We use geometry of Davis complex of a Coxeter group to prove the following result: if G is an infinite indecomposable Coxeter group and $H\subset G$ is a finite index reflection subgroup then the rank of H is not less than the rank of G. This generalizes results of math/0305093. We also describe some properties of the nerves of the group and the subgroup in the case of equal ranks.

v3: the proofs of Theorem 1 and Lemma 5 are corrected, an example added. 13 pages

References in corpus (1)

• On finite index reflection subgroups of discrete reflection groups

Cited by in corpus (9)

• Coxeter groups and meridional rank of links
• Coxeter groups, quiver mutations and geometric manifolds
• Essential hyperbolic Coxeter polytopes
• Equivariant triangulations of tori of compact Lie groups and hyperbolic extension to non-crystallographic Coxeter groups
• Hyperbolic subalgebras of hyperbolic Kac-Moody algebras
• Subspace stabilisers in hyperbolic lattices
• Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers
• Reflection subgroups of odd-angled Coxeter groups
• Bridge indices of spatial graphs and diagram colorings