Disordered arcs and Harer stability
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916548761878528 |
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| author | Harr, Oscar Vistrup, Max Wahl, Nathalie |
| author_facet | Harr, Oscar Vistrup, Max Wahl, Nathalie |
| contents | We give a new proof of homological stability with the best known isomorphism range for mapping class groups of surfaces with respect to genus. The proof uses the framework of Randal-Williams-Wahl and Krannich applied to disk stabilization in the category of bidecorated surfaces, using the Euler characteristic instead of the genus as a grading. The monoidal category of bidecorated surfaces does not admit a braiding, distinguishing it from previously known settings for homological stability. Nevertheless, we find that it admits a suitable Yang-Baxter element, which we show is sufficient structure for homological stability arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03858 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Disordered arcs and Harer stability Harr, Oscar Vistrup, Max Wahl, Nathalie Geometric Topology Algebraic Topology We give a new proof of homological stability with the best known isomorphism range for mapping class groups of surfaces with respect to genus. The proof uses the framework of Randal-Williams-Wahl and Krannich applied to disk stabilization in the category of bidecorated surfaces, using the Euler characteristic instead of the genus as a grading. The monoidal category of bidecorated surfaces does not admit a braiding, distinguishing it from previously known settings for homological stability. Nevertheless, we find that it admits a suitable Yang-Baxter element, which we show is sufficient structure for homological stability arguments. |
| title | Disordered arcs and Harer stability |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2211.03858 |