Finiteness properties of the Torelli group of surfaces with 2 boundary components
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911363701407744 |
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| author | Stylianakis, Charalampos |
| author_facet | Stylianakis, Charalampos |
| contents | In this paper we prove that the Torelli group of a surface of genus at least 3 with 2 boundary components is finitely generated. As a consequence, we answer Putman's question on the finite generation of the stabilizer subgroup of the Torelli group of a non separating simple closed curve. Furthermore, we prove that the Johnson's kernel is finitely generated if the genus of the surface is at least 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05834 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finiteness properties of the Torelli group of surfaces with 2 boundary components Stylianakis, Charalampos Geometric Topology Group Theory In this paper we prove that the Torelli group of a surface of genus at least 3 with 2 boundary components is finitely generated. As a consequence, we answer Putman's question on the finite generation of the stabilizer subgroup of the Torelli group of a non separating simple closed curve. Furthermore, we prove that the Johnson's kernel is finitely generated if the genus of the surface is at least 5. |
| title | Finiteness properties of the Torelli group of surfaces with 2 boundary components |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2601.05834 |