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Quantifying separability in RAAGs via representations

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arxiv 2403.17964 v2 pith:LGCDHTWB submitted 2024-03-14 math.GR math.GT

Olga Kharlampovich , Alina Vdovina This is my paper · ORCID
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We answer the question asked by Louder, McReynolds and Patel, and prove the following statement. Let L be a RAAG, 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, a fundamental groups of a hyperbolic 3-manifold.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Matrix entries, unipotents, and linearity of amalgams

    math.GR 2026-03 conditional novelty 8.0 of 10

    A matrix-entry criterion proves when doubles of linear groups stay linear, and superrigidity shows when they must not, yielding new residually finite non-linear groups.

  2. On transversality in flag manifolds and linearity of amalgams

    math.GR 2026-07 conditional novelty 6.0 of 10

    Doubles of negatively curved locally symmetric manifolds along primitive closed geodesics have linear fundamental groups; more generally, doubles of transverse subgroups are linear.

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