发表机构
Yau Mathematical Sciences Center, Tsinghua University; Beijing International Center for Mathematical Research, Peking University; Department of Mathematics, The University of Maryland at College Park（清华大学丘成桐数学科学中心; 北京大学北京国际数学研究中心; 马里兰大学帕克分校数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立了带边界定向拓扑4-流形中嵌入弧空间基本群的Dax同构，并证明在光滑情形下该同构与光滑版本一致，从而其同态不依赖光滑结构。
AI 中文摘要
设$X$为带边界的定向拓扑$4$-流形。我们建立了$X$中嵌入弧空间基本群的Dax同构。这里，嵌入空间可以是局部平坦嵌入的单纯集，也可以是赋予紧开拓扑的拓扑嵌入空间。当$X$光滑时，我们证明光滑弧空间与拓扑弧空间的基本群具有典范同构，且拓扑Dax同构与光滑Dax同构一致。因此，光滑Dax同构中出现的同态不依赖于光滑结构。
英文摘要
Let $X$ be an oriented topological $4$-manifold with boundary. We establish a Dax isomorphism for the fundamental group of the space of embedded arcs in $X$. Here, the embedding space can be either the simplicial set of locally flat embeddings or the space of topological embeddings endowed with the compact-open topology. When $X$ is smooth, we show that the space of smooth arcs and topological arcs have canonically isomorphic fundamental groups, and the topological Dax isomorphism agrees with the smooth Dax isomorphism. As a consequence, the homomorphisms that arise in the smooth Dax isomorphism do not depend on the smooth structure.
Comments16 pages; comments are welcome!
