Homomorphisms of commutator subgroups of braid groups with small number of strings
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866916504649334784 |
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| author | Orevkov, S. Yu. |
| author_facet | Orevkov, S. Yu. |
| contents | For any $n$, we describe all endomorphisms of the braid group $B_n$ and of its commutator subgroup $B'_n$, as well as all homomorphisms $B'_n\to B_n$. These results are new only for small $n$ because endomorphisms of $B_n$ are already described by Castel for $n\ge 6$, and homomorphisms $B'_n\to B_n$ and endomorphisms of $B'_n$ are already described by Kordek and Margalit for $n\ge 7$. We use very different approaches for $n=4$ and for $n\ge 5$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2010_02446 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Homomorphisms of commutator subgroups of braid groups with small number of strings Orevkov, S. Yu. Group Theory For any $n$, we describe all endomorphisms of the braid group $B_n$ and of its commutator subgroup $B'_n$, as well as all homomorphisms $B'_n\to B_n$. These results are new only for small $n$ because endomorphisms of $B_n$ are already described by Castel for $n\ge 6$, and homomorphisms $B'_n\to B_n$ and endomorphisms of $B'_n$ are already described by Kordek and Margalit for $n\ge 7$. We use very different approaches for $n=4$ and for $n\ge 5$. |
| title | Homomorphisms of commutator subgroups of braid groups with small number of strings |
| topic | Group Theory |
| url | https://arxiv.org/abs/2010.02446 |