Kaydedildi:
| Yazar: | |
|---|---|
| Materyal Türü: | Preprint |
| Baskı/Yayın Bilgisi: |
2020
|
| Konular: | |
| Online Erişim: | https://arxiv.org/abs/2012.05993 |
| Etiketler: |
Etiketle
Etiket eklenmemiş, İlk siz ekleyin!
|
| _version_ | 1866916150684680192 |
|---|---|
| author | Vlamis, Nicholas G. |
| author_facet | Vlamis, Nicholas G. |
| contents | We prove that the mapping class group of a surface obtained from removing a Cantor set from either the 2-sphere, the plane, or the interior of the closed 2-disk has no proper countable-index subgroups. The proof is an application of the automatic continuity of these groups, which was established by Mann. As corollaries, we see that these groups do not contain any proper finite-index subgroups and that each of these groups have trivial abelianization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_05993 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Three perfect mapping class groups Vlamis, Nicholas G. Geometric Topology Group Theory We prove that the mapping class group of a surface obtained from removing a Cantor set from either the 2-sphere, the plane, or the interior of the closed 2-disk has no proper countable-index subgroups. The proof is an application of the automatic continuity of these groups, which was established by Mann. As corollaries, we see that these groups do not contain any proper finite-index subgroups and that each of these groups have trivial abelianization. |
| title | Three perfect mapping class groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2012.05993 |