Operadic actions on long knots and 2-string links
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929438703222784 |
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| author | Batelier, Etienne Ducoulombier, Julien |
| author_facet | Batelier, Etienne Ducoulombier, Julien |
| contents | In the present work, we realize the space of 2-string links $\mathcal{L}$ as a free algebra over a colored operad denoted $\mathcal{SCL}$ (for "Swiss-Cheese for links"). This result extends works of Burke and Koytcheff about the quotient of $\mathcal{L}$ by its center and is compatible with Budney's freeness theorem for long knots. From an algebraic point of view, our main result refines Blaire, Burke and Koytcheff's theorem on the monoid of isotopy classes of string links. Topologically, it expresses the homotopy type of the isotopy class of a 2-string link in terms of the homotopy types of the classes of its prime factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_06036 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Operadic actions on long knots and 2-string links Batelier, Etienne Ducoulombier, Julien Algebraic Topology Geometric Topology 18D50, 57M25, 55U40, 57R40 In the present work, we realize the space of 2-string links $\mathcal{L}$ as a free algebra over a colored operad denoted $\mathcal{SCL}$ (for "Swiss-Cheese for links"). This result extends works of Burke and Koytcheff about the quotient of $\mathcal{L}$ by its center and is compatible with Budney's freeness theorem for long knots. From an algebraic point of view, our main result refines Blaire, Burke and Koytcheff's theorem on the monoid of isotopy classes of string links. Topologically, it expresses the homotopy type of the isotopy class of a 2-string link in terms of the homotopy types of the classes of its prime factors. |
| title | Operadic actions on long knots and 2-string links |
| topic | Algebraic Topology Geometric Topology 18D50, 57M25, 55U40, 57R40 |
| url | https://arxiv.org/abs/2005.06036 |