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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.
Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homological conformal field theory. This means in particular that it admit
We give a complete list of the cobounded actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces up to a natural equivalence relation. The set of equivalence classes carries a natural partial order first introduced by Abbott-Balasubra
The following is an amalgamation of four preprints and some computer programs which together represent the current state of our investigations of higher order links. This investigation was motivated by questions discussed and raised in the first auth
In this paper we give a simple proof of the equivalence between the rational link associated to the continued fraction $left[ a_{1},a_{2},cdots a_{m}right],$ $a_{i}inmathbb{N}$, and the two bridge link of type $p/q,$ where $p/q$ is the rational given
We study configuration space integral formulas for Milnors homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a certain space of