Felikson, Anna Tumarkin, Pavel 2009-09-18 We use the geometry of the Davis complex of a Coxeter group to investigate finite index reflection subgroups of Coxeter groups. The main result is the following: 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 earlier results of the authors (2004). We also describe the relationship between the nerves of the group and the subgroup in the case of equal rank application/pdf https://folia.unifr.ch/global/documents/301410 https://folia.unifr.ch/documents/301410/files/felikson_rsc.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9947-09-04859-4 info:eu-repo/semantics/openAccess License undefined Transactions of the American Mathematical Society. - 2010, vol. 362, p. 847-858. info:eu-repo/classification/udc/51 Reflection subgroups of Coxeter groups http://purl.org/coar/resource_type/c_6501