用于拼接的操作数
An operad for splicing
摘要：
引入了一种新的拓扑操作数，称为拼接操作数。这个操作作用于一个广泛的自嵌入空间类N -> N，其中N是一个流形。这个操作数在EC（j，M）上的作用（自嵌入R^j x M --> R^j x M，支持在I^j x M中）是（j+1）-立方体操作数在这个空间上的作用的扩展。此外，剪接操作数的作用编码了拉里·西本曼在j=1，M=D^2的情况下对S^3中结点的剪接构造。R^3中的长结点空间（记为K_{3,1}）被证明是一个具有自由生成子空间P的自由2-立方体对象，该子空间P是长结点的子空间，它相对于连通和运算是素的。本文的主要结果之一是，K_{3,1}是自由的拼接操作数的作用，但自由生成空间是更“小”的空间环面和双曲结TH \subset K_{3,1}。此外，K_{3,1}的剪接操作数具有作为操作数的“简单”同伦类型。
英文摘要：
A new topological operad is introduced, called the splicing operad. This operad acts on a broad class of spaces of self-embeddings N --> N where N is a manifold. The action of this operad on EC(j,M) (self embeddings R^j x M --> R^j x M with support in I^j x M) is an extension of the action of the operad of (j+1)-cubes on this space. Moreover the action of the splicing operad encodes Larry Siebenmann's splicing construction for knots in S^3 in the j=1, M=D^2 case. The space of long knots in R^3 (denoted K_{3,1}) was shown to be a free 2-cubes object with free generating subspace P, the subspace of long knots that are prime with respect to the connect-sum operation. One of the main results of this paper is that K_{3,1} is free with respect to the splicing operad action, but the free generating space is the much `smaller' space of torus and hyperbolic knots TH \subset K_{3,1}. Moreover, the splicing operad for K_{3,1} has a `simple' homotopy-type as an operad.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
