Geodesic
Operadic actions on long knots and 2–string links
Batelier, Etienne1 ; Ducoulombier, Julien2
1 Mathematisches Institut, Universität Münster, Münster, Germany
2 Université Sorbonne Paris Nord, Villetaneuse, France
Algebraic and Geometric Topology, Tome 23 (2023) no. 2, pp. 833-882

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We realize the space of 2–string links ℒ as a free algebra over a colored operad denoted by 𝒮𝒞ℒ (for “Swiss-cheese for links”). This result extends works of Burke and Koytcheff about the quotient of 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.

DOI : 10.2140/agt.2023.23.833
Keywords: space of knots, space of links, little cubes operad, Swiss-cheese operad, embedding, homotopy theory

Batelier, Etienne 1 ; Ducoulombier, Julien 2

1 Mathematisches Institut, Universität Münster, Münster, Germany
2 Université Sorbonne Paris Nord, Villetaneuse, France 
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Batelier, Etienne; Ducoulombier, Julien. Operadic actions on long knots and 2–string links. Algebraic and Geometric Topology, Tome 23 (2023) no. 2, pp. 833-882. doi: 10.2140/agt.2023.23.833

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