Cubulated hyperbolic groups admit Anosov representations

作者：Sami Douba, Balthazar Fléchelles, Theodore Weisman, Feng Zhu · 发表于：Geometry & Topology · 年份：2025 · DOI：10.2140/gt.2025.29.4695 · 被引用次数：3 · 研究领域：Geometric and Algebraic Topology、Advanced Algebra and Geometry、Homotopy and Cohomology in Algebraic Topology

We prove that any hyperbolic group acting properly discontinuously and cocompactly on a CAT.0/ cube complex admits a projective Anosov representation into SL.d;R/ for some d .More specifically, we show that if is a hyperbolic quasiconvex subgroup of a right-angled Coxeter group C , then a generic representation of C by reflections restricts to a projective Anosov representation of .22E40; 20F55, 20F67 1. Introduction 4695 2. Cube complexes and right-angled Coxeter groups 4701 3. Bounded product projections 4708 4. Reflection groups acting on convex projective domains 4713 5. Walls and half-cones in reflection domains 4718 6. Singular values, stable and unstable subspaces, and regularity 4727 7. Stable and unstable subspaces in half-cones 4733 8. Proof of the main theorem 4737 Appendix.Failure of strong nesting for half-cones 4755