关于“小测地线”与自由闭路空间
On "small geodesics" and free loop spaces
摘要：
构造了一个拓扑群，它同伦等价于路连通黎曼流形$M$上的点闭路空间，并由$M$上的“可组合小测地线”给出.这个模型类似于J. Milnor的自由群构造\cite{Milnor}，它为连通单纯复形的点闭路空间提供了一个模型。相关的函数空间是从“可组合的小测地线”，它提供了模型的自由闭路空间的$M$以及空间的连续映射从表面到$M$。
英文摘要：
A topological group is constructed which is homotopy equivalent to the pointed loop space of a path-connected Riemannian manifold $M$ and which is given in terms of "composable small geodesics" on $M$. This model is analogous to J. Milnor's free group construction \cite{Milnor} which provides a model for the pointed loop space of a connected simplicial complex. Related function spaces are constructed from "composable small geodesics" which provide models for the free loop space of $M$ as well as the space of continuous maps from a surface to $M$.
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。
