高维的劈裂运算与弦拓扑
The Cleavage Operad and String Topology of Higher Dimension
摘要：
对于嵌入在欧几里得空间R^{n+1}中的流形N，我们产生一个作用于从N到M的映射空间的着色操作数，其中M是紧致的、定向的、光滑流形。对于单位球面N，我们指出这是如何给出同调作用的，推广了Cacti操作数的作用，并通过取N为R^2中的单位圆来恢复查斯-沙利文积。我们继续证明，对于R^{n+1}中的单位球面S^n，所构造的运算数是着色的E_{n+1} -运算数。这个E_{n+1} -结构最后被SO（n+1）扭曲，同调地给出框架小（n+1）-圆盘的作用。
英文摘要：
For a manifold N embedded inside euclidean space R^{n+1}, we produce a coloured operad that acts on the space of maps from N to M, where M is a compact, oriented, smooth manifold. For N the unit sphere, we indicate how this gives homological actions, generalizing the action of the Cacti operad and retrieving the Chas-Sullivan product by taking N to be the unit-circle in R^2. We go on to show that for S^n the unit sphere in R^{n+1}, the operad constructed is a coloured E_{n+1}-operad. This E_{n+1}-structure is finally twisted by SO(n+1) to homologically give actions of the framed little (n+1)-disks.
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。
