Which Immersions into Euclidean Space are Boundary Immersions?

Austin Konkel

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arXiv · 2610.25618

Which Immersions into Euclidean Space are Boundary Immersions?

Austin Konkel

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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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Austin Konkel. 2026-10-19. Which Immersions into Euclidean Space are Boundary Immersions?. https://arxiv.org/abs/2610.25618

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