Critical exponent gap and leafwise dimension
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915018624204800 |
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| author | Solan, Omri Nisan |
| author_facet | Solan, Omri Nisan |
| contents | We show that for every nonarithmetic lattice $Γ<{\rm SL}_2(\mathbb{C})$ there is a gap $\varepsilon_Γ>0$ such that for every $g\in {\rm SL}_2(\mathbb{C})$ the intersection ${\rm SL}_2(\mathbb{R})\cap gΓg^{-1}$ is either a lattice in ${\rm SL}_2(\mathbb{R})$ or has critical exponent $δ({\rm SL}_2(\mathbb{R})\cap gΓg^{-1}) \leq 1 - \varepsilon_Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical exponent gap and leafwise dimension Solan, Omri Nisan Dynamical Systems We show that for every nonarithmetic lattice $Γ<{\rm SL}_2(\mathbb{C})$ there is a gap $\varepsilon_Γ>0$ such that for every $g\in {\rm SL}_2(\mathbb{C})$ the intersection ${\rm SL}_2(\mathbb{R})\cap gΓg^{-1}$ is either a lattice in ${\rm SL}_2(\mathbb{R})$ or has critical exponent $δ({\rm SL}_2(\mathbb{R})\cap gΓg^{-1}) \leq 1 - \varepsilon_Γ$. |
| title | Critical exponent gap and leafwise dimension |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.00700 |