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arXiv · 2404.00700

Critical exponent gap and leafwise dimension

Omri Nisan Solan
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Abstract

We show that for every nonarithmetic lattice $\Gamma<{\rm SL}_2(\mathbb{C})$ there is a gap $\varepsilon_\Gamma>0$ such that for every $g\in {\rm SL}_2(\mathbb{C})$ the intersection ${\rm SL}_2(\mathbb{R})\cap g\Gamma g^{-1}$ is either a lattice in ${\rm SL}_2(\mathbb{R})$ or has critical exponent $\delta({\rm SL}_2(\mathbb{R})\cap g\Gamma g^{-1}) \leq 1 - \varepsilon_\Gamma$.

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Omri Nisan Solan. 2024-03-31. Critical exponent gap and leafwise dimension. https://arxiv.org/abs/2404.00700

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