Homomorphisms between XL-type Artin groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913745378213888 |
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| author | Blufstein, Martín Martin, Alexandre Vaskou, Nicolas |
| author_facet | Blufstein, Martín Martin, Alexandre Vaskou, Nicolas |
| contents | We study homomorphisms between XL-type Artin groups and show that, in a suitable sense, a generic Artin group is both hopfian and co-hopfian.
For XL-type Artin groups over complete graphs, we describe all possible homomorphisms with sufficiently large image, and prove in particular that such groups are both hopfian and co-hopfian. For Artin groups over general graphs with all labels at least $6$, we characterise in terms of the presentation graph exactly when these groups are co-hopfian, as well as when they have a finite outer automorphism group. When in addition the presentation graph has no cut-vertex, we show that their automorphism group is finitely generated and we provide a generating set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19091 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homomorphisms between XL-type Artin groups Blufstein, Martín Martin, Alexandre Vaskou, Nicolas Group Theory 20F65, 20F36, 20F67, 20F28 We study homomorphisms between XL-type Artin groups and show that, in a suitable sense, a generic Artin group is both hopfian and co-hopfian. For XL-type Artin groups over complete graphs, we describe all possible homomorphisms with sufficiently large image, and prove in particular that such groups are both hopfian and co-hopfian. For Artin groups over general graphs with all labels at least $6$, we characterise in terms of the presentation graph exactly when these groups are co-hopfian, as well as when they have a finite outer automorphism group. When in addition the presentation graph has no cut-vertex, we show that their automorphism group is finitely generated and we provide a generating set. |
| title | Homomorphisms between XL-type Artin groups |
| topic | Group Theory 20F65, 20F36, 20F67, 20F28 |
| url | https://arxiv.org/abs/2410.19091 |