Torsion at the Threshold for Mapping Class Groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910599911309312 |
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| author | Jekel, Solomon Rolland, Rita Jiménez |
| author_facet | Jekel, Solomon Rolland, Rita Jiménez |
| contents | The mapping class group $Γ_g^ 1$ of a closed orientable surface of genus $g \geq 1$ with one marked point can be identified, by the Nielsen action, with a subgroup of the group of orientation preserving homeomorphims of the circle. This inclusion pulls back the powers of the discrete universal Euler class producing classes $\text{E}^n \in H^{2n}(Γ_g^1;\mathbb{Z})$ for all $n\geq 1$. In this paper we study the power $n=g,$ and prove: $\text{E}^g$ is a torsion class which generates a cyclic subgroup of $H^{2g}(Γ_g^1;\mathbb{Z})$ whose order is a positive integer multiple of $4g(2g+1)(2g-1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Torsion at the Threshold for Mapping Class Groups Jekel, Solomon Rolland, Rita Jiménez Geometric Topology Algebraic Topology The mapping class group $Γ_g^ 1$ of a closed orientable surface of genus $g \geq 1$ with one marked point can be identified, by the Nielsen action, with a subgroup of the group of orientation preserving homeomorphims of the circle. This inclusion pulls back the powers of the discrete universal Euler class producing classes $\text{E}^n \in H^{2n}(Γ_g^1;\mathbb{Z})$ for all $n\geq 1$. In this paper we study the power $n=g,$ and prove: $\text{E}^g$ is a torsion class which generates a cyclic subgroup of $H^{2g}(Γ_g^1;\mathbb{Z})$ whose order is a positive integer multiple of $4g(2g+1)(2g-1)$. |
| title | Torsion at the Threshold for Mapping Class Groups |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2409.07311 |