Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$

Elon Lindenstrauss; Amir Mohammadi

Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$

Dynamical Systems 2022-06-07 v2 Geometric Topology Metric Geometry

Authors: Elon Lindenstrauss , Amir Mohammadi

Abstract

We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of $\operatorname{SL}_2(\mathbb R)$ in arithmetic quotients of $\operatorname{SL}_2(\mathbb C)$ and $\operatorname{SL}_2(\mathbb R)\times\operatorname{SL}_2(\mathbb R)$ . The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.

Keywords

effective density polynomial error rate upper triangular subgroup arithmetic quotients margulis function spectral gap

Cite

@article{arxiv.2112.14562,
  title  = {Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$},
  author = {Elon Lindenstrauss and Amir Mohammadi},
  journal= {arXiv preprint arXiv:2112.14562},
  year   = {2022}
}

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76 pages

Polynomial effective density in quotients of $\mathbb H^3$ and $\mathbb H^2\times\mathbb H^2$

Abstract

Keywords

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