Doubles of negatively curved locally symmetric manifolds along primitive closed geodesics have linear fundamental groups; more generally, doubles of transverse subgroups are linear.
Quantifying separability in RAAGs via representations
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abstract
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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2026 1verdicts
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On transversality in flag manifolds and linearity of amalgams
Doubles of negatively curved locally symmetric manifolds along primitive closed geodesics have linear fundamental groups; more generally, doubles of transverse subgroups are linear.