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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2511.21259 |
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| _version_ | 1866917106467995648 |
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| author | Terron, Susanna |
| author_facet | Terron, Susanna |
| contents | We extend Jones' construction to obtain a surjective map from the Brown-Thompson group $F_3$ to the set of pointed links up to pointed isotopy. We then introduce an operation on $F_3$, and use it to define a new monoid $(F_3, \diamond)$, called the central monoid. Using the extended version of Jones' construction, we obtain a surjective monoid homomorphism from the central monoid to the monoid of pointed links with connected sum. This allows us to introduce a standard form for connected sum representatives in $F_3$, and we extend this construction to a certain family of links by defining disjoint union and linking moves on $F_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21259 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing Thompson representatives via pointed links Terron, Susanna Geometric Topology Group Theory 57K10, 20F65 We extend Jones' construction to obtain a surjective map from the Brown-Thompson group $F_3$ to the set of pointed links up to pointed isotopy. We then introduce an operation on $F_3$, and use it to define a new monoid $(F_3, \diamond)$, called the central monoid. Using the extended version of Jones' construction, we obtain a surjective monoid homomorphism from the central monoid to the monoid of pointed links with connected sum. This allows us to introduce a standard form for connected sum representatives in $F_3$, and we extend this construction to a certain family of links by defining disjoint union and linking moves on $F_3$. |
| title | Constructing Thompson representatives via pointed links |
| topic | Geometric Topology Group Theory 57K10, 20F65 |
| url | https://arxiv.org/abs/2511.21259 |