论文标题
长结和2弦链接的行动行动
Operadic actions on long knots and 2-string links
论文作者
论文摘要
在目前的工作中，我们意识到2弦链接的空间$ \ Mathcal {l} $作为彩色的Operad表示$ \ MATHCAL {SCL} $的免费代数（对于“ Swiss-Cheese for Links”）。该结果扩展了Burke和Koytcheff的作品，内容涉及其中心的$ \ Mathcal {l} $的商，并且与Budney的Freeness定理兼容了长结。从代数的角度来看，我们的主要结果完善了Blaire，Burke和Koytcheff的弦线链接类别类别的定理。从拓扑上讲，它表达了2弦链路的同位素类别的同位素类型，该类别的同型类型的类型的类型的类型。
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.
