Topology Seminar

Lorenzo RuffoniTufts University
Incoherence for right-angled Coxeter groups on surfaces

Tuesday, November 28, 2023 - 2:55pm
Malott 206

A group is "coherent" if every finitely generated subgroup is finitely presented. In a certain sense, coherence is a low-dimensional phenomenon. For instance, 3-manifold groups and one-relator groups are coherent. In this talk we consider Coxeter groups defined by a graph that is a flag triangulation of a surface of genus g. For each g>0, we construct a Coxeter group that is right-angled, hyperbolic, and incoherent. In these examples the witness to incoherence is always the fiber in a virtual algebraic fibration. This provides positive evidence towards a variation on Singer's Conjecture for right-angled Coxeter groups proposed by Davis-Okun. This is joint work with Genevieve Walsh.