Groups Geometry and Dynamics· 2026Q1
Quantifying separability in RAAGs via representations
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- 2026year
Short summary
A finite-dimensional representation of a right-angled Artin group (RAAG) can separate a word quasiconvex subgroup H in the induced Zariski topology.
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Key points
- A finite-dimensional representation can separate word quasiconvex subgroups in RAAGs.
- A polynomial upper bound is established for the size of quotients used in this separation.
- The result applies to virtually special groups and fundamental groups of hyperbolic 3-manifolds.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Groups Geometry and Dynamics, 2026 · DOI ↗
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