Work

Quantifying separability in RAAGs via representations

Year: 2026

Type: article

Abstract: We answer the question raised by Louder, McReynolds and Patel in their 2017 article and prove the following statement. Let L be a right-angled Artin group (abbreviated as RAAG) and H a word quasiconvex subgroup of L ; then there is a finite-dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L . This implies the same statement for a virtually special group L , and, in particular, for the fundamental groups of a hyperbolic 3 -manifold.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/1006

Authors: Olga Kharlampovich, Alina Vdovina

Institutions: The Graduate Center, CUNY, Hunter College, City College of New York, City University of New York

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: City University of New York

OpenAlex ID: W4393299802

FWCI:

Cites:

Cited by:

Related to: 10