In the present work, we realize the space of string 2-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 Budneys freeness theorem for long knots. From an algebraic point of view, our main result refines Blaire, Burke and Koytcheffs theorem on the monoid of isotopy classes of string links. Topologically, it expresses the homotopy type of the isotopy class of a string 2-link in terms of the homotopy types of the classes of its prime factors.
تحميل البحث