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| Autori principali: | , |
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| Natura: | Preprint |
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2022
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| Accesso online: | https://arxiv.org/abs/2201.09187 |
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| _version_ | 1866908649039855616 |
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| author | Caprau, Carmen Yeung, Antonia |
| author_facet | Caprau, Carmen Yeung, Antonia |
| contents | We show that the virtual singular braid monoid on $n$ strands embeds in a group $VSG_n$, which we call the virtual singular braid group on $n$ strands. The group $VSG_n$ contains a normal subgroup $VSPG_n$ of virtual singular pure braids. We show that $VSG_n$ is a semi-direct product of $VSPG_n$ and the symmetric group $S_n$. We provide a presentation for $VSPG_n$ via generators and relations. We also represent $VSPG_n$ as a semi-direct product of $n-1$ subgroups and study the structures of these subgroups. These results yield a normal form of words in the virtual singular braid group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_09187 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Algebraic structures among virtual singular braids Caprau, Carmen Yeung, Antonia Geometric Topology Group Theory We show that the virtual singular braid monoid on $n$ strands embeds in a group $VSG_n$, which we call the virtual singular braid group on $n$ strands. The group $VSG_n$ contains a normal subgroup $VSPG_n$ of virtual singular pure braids. We show that $VSG_n$ is a semi-direct product of $VSPG_n$ and the symmetric group $S_n$. We provide a presentation for $VSPG_n$ via generators and relations. We also represent $VSPG_n$ as a semi-direct product of $n-1$ subgroups and study the structures of these subgroups. These results yield a normal form of words in the virtual singular braid group. |
| title | Algebraic structures among virtual singular braids |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2201.09187 |