2025/02/18 by Jean‐François Lafont, Barry Minemyer, Lafont, Jean-Francois +7
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2502.12906
openalex publication_date 2025/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over ℤ that is flexible enough to yield infinitely many isomorphism classes in each virtual cohomological dimension (vcd) n≥ 2. Our procedure combines results of Jankiewicz, Norin, and Wise with a generalization of a construction due to Osajda involving a new simplicial thickening process. We also give a topological argument showing that the vcd of the right-angled Coxeter groups produced by our construction increases by exactly one with each iteration, guaranteeing that our process produces examples of every vcd.