PreprintarXiv licencearXiv
Which Immersions into Euclidean Space are Boundary Immersions?
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.
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BibTeX
@misc{konkel2026which,
title = {{Which Immersions into Euclidean Space are Boundary Immersions?}},
author = {Austin Konkel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25618},
eprint = {2610.25618},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25618},
}
RIS
TY - UNPB
TI - Which Immersions into Euclidean Space are Boundary Immersions?
AU - Austin Konkel
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25618
UR - https://arxiv.org/abs/2610.25618
AB - 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.
ER -