The volumes of the Hitchin-Riemann moduli spaces are infinite
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910868353056768 |
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| author | Choi, Suhyoung Jung, Hongtaek |
| author_facet | Choi, Suhyoung Jung, Hongtaek |
| contents | In this study, we prove that the actions of the mapping class groups on a large range of higher Teichmüller spaces with a rank of at least two possess infinite Atiyah-Bott-Goldman covolume. This result encompasses $\mathsf{G}$-Hitchin components of a higher rank split real form $\mathsf{G}$ and each component of the space of $\mathsf{Sp}_{2n}(\mathbb{R})$-maximal representations where $n \geq 2$. To achieve this outcome, we employ Goldman flows to find an infinite series of subsets of identical volume, the images of which in the quotient space are all mutually disjoint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10093 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The volumes of the Hitchin-Riemann moduli spaces are infinite Choi, Suhyoung Jung, Hongtaek Geometric Topology Primary 53D30, Secondary 57K20 In this study, we prove that the actions of the mapping class groups on a large range of higher Teichmüller spaces with a rank of at least two possess infinite Atiyah-Bott-Goldman covolume. This result encompasses $\mathsf{G}$-Hitchin components of a higher rank split real form $\mathsf{G}$ and each component of the space of $\mathsf{Sp}_{2n}(\mathbb{R})$-maximal representations where $n \geq 2$. To achieve this outcome, we employ Goldman flows to find an infinite series of subsets of identical volume, the images of which in the quotient space are all mutually disjoint. |
| title | The volumes of the Hitchin-Riemann moduli spaces are infinite |
| topic | Geometric Topology Primary 53D30, Secondary 57K20 |
| url | https://arxiv.org/abs/2305.10093 |