A generating set for the Johnson kernel
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909675491950592 |
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| author | Boggi, Marco |
| author_facet | Boggi, Marco |
| contents | For a connected orientable hyperbolic surface $S$ without boundary and of finite topological type, the Johnson kernel ${\mathcal K}(S)$ is the subgroup of the mapping class group of $S$ generated by Dehn twists about separating simple closed curves on $S$. We prove that ${\mathcal K}(S)$ is generated by the Dehn twists about separating simple closed curves on $S$ bounding either: a closed subsurface of genus $1$ or $2$; a closed subsurface of genus $1$ minus one point; a closed disc minus two points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generating set for the Johnson kernel Boggi, Marco Geometric Topology For a connected orientable hyperbolic surface $S$ without boundary and of finite topological type, the Johnson kernel ${\mathcal K}(S)$ is the subgroup of the mapping class group of $S$ generated by Dehn twists about separating simple closed curves on $S$. We prove that ${\mathcal K}(S)$ is generated by the Dehn twists about separating simple closed curves on $S$ bounding either: a closed subsurface of genus $1$ or $2$; a closed subsurface of genus $1$ minus one point; a closed disc minus two points. |
| title | A generating set for the Johnson kernel |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2507.01560 |