Edge subdivisions and the L2‐homology of right‐angled Coxeter groups
Abstract
Abstract If is a flag triangulation of , then the Davis complex for the associated right‐angled Coxeter group (RACG) is a contractible ‐manifold. A special case of a conjecture of Singer predicts that the ‐homology of such vanishes outside the middle dimension. We give conditions which guarantee this vanishing is preserved under edge subdivision of . In particular, we verify Singer's conjecture when is the barycentric subdivision of the boundary of an ‐simplex and for general barycentric subdivisions of triangulations of . Using this, we construct explicit counterexamples to a torsion‐growth analogue of Singer's conjecture.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 114
- Issue
- 1
- Publication date
- 1 July 2026
- Language
- EN