Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Lin, Jianfeng, Xie, Yi, Zhang, Boyu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213337679