The Andersen-Masbaum-Ueno conjecture for the derived subgroup of the Johnson kernel
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914433944518656 |
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| author | Detcherry, Renaud |
| author_facet | Detcherry, Renaud |
| contents | A conjecture of Andersen, Masbaum and Ueno states that for any compact oriented surface $Σ_{g,n}$ and any pseudo-Anosov $f\in \mathrm{Mod}(Σ_{g,n}),$ the matrix $ρ_r(f)$ has infinite order for any large $r,$ where $ρ_r$ is the $\mathrm{SO}(3)$-WRT quantum representation of the mapping class group $\mathrm{Mod}(Σ_{g,n})$ at a primitive $r$-th root of unity.
We prove this conjecture for prime $r$ and any $f\in [J_2(Σ_{g,n}),J_2(Σ_{g,n})],$ where $J_2(Σ_{g,n})$ is the Johnson kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Andersen-Masbaum-Ueno conjecture for the derived subgroup of the Johnson kernel Detcherry, Renaud Geometric Topology Representation Theory A conjecture of Andersen, Masbaum and Ueno states that for any compact oriented surface $Σ_{g,n}$ and any pseudo-Anosov $f\in \mathrm{Mod}(Σ_{g,n}),$ the matrix $ρ_r(f)$ has infinite order for any large $r,$ where $ρ_r$ is the $\mathrm{SO}(3)$-WRT quantum representation of the mapping class group $\mathrm{Mod}(Σ_{g,n})$ at a primitive $r$-th root of unity. We prove this conjecture for prime $r$ and any $f\in [J_2(Σ_{g,n}),J_2(Σ_{g,n})],$ where $J_2(Σ_{g,n})$ is the Johnson kernel. |
| title | The Andersen-Masbaum-Ueno conjecture for the derived subgroup of the Johnson kernel |
| topic | Geometric Topology Representation Theory |
| url | https://arxiv.org/abs/2603.29397 |