Embedding punctured n-manifolds in Euclidean (2n-1)-space

TL;DR

This paper classifies how punctured orientable n-manifolds can be embedded into Euclidean space of dimension 2n-1, extending previous classification results for such embeddings.

Contribution

It provides a comprehensive classification of embeddings of punctured n-manifolds into Euclidean (2n-1)-space, generalizing earlier work by Becker-Glover and Saeki.

Findings

Complete classification of embeddings up to isotopy

Extension of classical embedding results to punctured manifolds

New insights into the topology of high-dimensional manifold embeddings

Abstract

Let $N$ be a closed orientable connected $n$-manifold, $n\ge 4$. We classify embeddings of the punctured manifold $N_0$ into $\R^{2n-1}$ up to isotopy. Our result in some sense extends results of J.C. Becker -- H.H. Glover (1971) and O. Saeki (1999).