Year: 2026
Type: preprint
Abstract: Here we study the problem of whether a given codimension one immersion $f$ of a closed and connected manifold into Euclidean space can be extended to an equidimensional immersion $F$ of some compact manifold $M$ whose restriction to the boundary parameterizes the image $S$ of $f$. Such an extension $F$ exists if and only if (i) simple conditions on orientations and wrapping numbers are satisfied and (ii) a distinguished finite subset of the first cohomology of $S$ with coefficients in a certain sheaf of finite groups contains the preferred point.
Source: arXiv (Cornell University)
Author: Konkel, Austin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223038038