Zariski closures of linear reflection groups

Abstract: We show that linear reflection groups in the sense of Vinberg are often Zariski dense in \(\mathrm{PGL}(n)\). Among the applications are examples of low-dimensional closed hyperbolic manifolds whose fundamental groups virtually embed as Zariski-dense subgroups of \(\mathrm{SL}(n,\mathbb{Z})\), as well as some one-ended Zariski-dense subgroups of \(\mathrm{SL}(n,\mathbb{Z})\) that are finitely generated but infinitely presented, for all sufficiently large \(n\).

This is joint work with Jacques Audibert, Gye-Seon Lee, and Ludovic Marquis.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

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