Thin right‐angled Coxeter groups in some uniform arithmetic lattices

@article{Douba2022ThinRC,
  title={Thin right‐angled Coxeter groups in some uniform arithmetic lattices},
  author={Sami Douba},
  journal={Bulletin of the London Mathematical Society},
  year={2022}
}
  • Sami Douba
  • Published 14 November 2021
  • Mathematics
  • Bulletin of the London Mathematical Society
. Using a variant of an unpublished argument due to Agol, we show that an irreducible right-angled Coxeter group on n ≥ 3 vertices embeds as a thin subgroup of a uniform arithmetic lattice in an indefinite orthogonal group O( p,q ) for some p,q ≥ 1 satisfying p + q = n . 

A hyperbolic lattice in each dimension with Zariski-dense surface subgroups

. For each integer n ≥ 3, we exhibit a nonuniform arithmetic lattice in SO( n, 1) containing Zariski-dense surface subgroups.

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