映射空间的Chen模型及其曲面积
A Chen model for mapping spaces and the surface product
摘要：
我们开发了一个机器的陈迭代积分更高的Hochschild复杂。这些复合物的微分是仿照一个任意的单纯集，以同样的方式普通Hochschild微分是仿照圆。利用这些定理给出了一般映射空间的代数模型，定义并研究了所有亏格曲面到流形的映射空间的同调上的面积运算。这是弦拓扑中的圈积的类似物。作为应用，我们证明了该乘积是同伦不变量的。我们证明了Hochschild-Kostant-Rosenberg型定理，并利用它们给出了奇球面和李群的曲面积的显式公式。
英文摘要：
We develop a machinery of Chen iterated integrals for higher Hochschild complexes. These are complexes whose differentials are modeled on an arbitrary simplicial set much in the same way the ordinary Hochschild differential is modeled on the circle. We use these to give algebraic models for general mapping spaces and define and study the surface product operation on the homology of mapping spaces of surfaces of all genera into a manifold. This is an analogue of the loop product in string topology. As an application, we show this product is homotopy invariant. We prove Hochschild-Kostant-Rosenberg type theorems and use them to give explicit formulae for the surface product of odd spheres and Lie groups.
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。
