论文标题
自由循环空间的代数模型
An algebraic model for the free loop space
论文作者
论文摘要
我们描述了一个代数链级结构，该结构将从任意拓扑空间到其自由环空间的通道建模。该结构的输入是一个分类的煤堡，即满足某些特性的弯曲煤层，输出是链复合物。该结构是差分（DG）山地的Cohochschild综合体的修改版本。当适当解释的任意简单集$ x $上的链条上应用于链条时，它会产生一个链条复合体，该复合物自然是准iSmormorphic的，在$ x $的几何实现的自由环空间上，奇异的链条。我们将这种结构与使用DG Hopf代数模型的伴随动作构建的自由环空间的扭曲张量产品模型相关联。
We describe an algebraic chain level construction that models the passage from an arbitrary topological space to its free loop space. The input of the construction is a categorical coalgebra, i.e. a curved coalgebra satisfying certain properties, and the output is a chain complex. The construction is a modified version of the coHochschild complex of a differential graded (dg) coalgebra. When applied to the chains on an arbitrary simplicial set $X$, appropriately interpreted, it yields a chain complex that is naturally quasi-isomorphic to the singular chains on the free loop space of the geometric realization of $X$. We relate this construction to a twisted tensor product model for the free loop space constructed using the adjoint action of a dg Hopf algebra model for the based loop space.
