Spin structures and codimension two embeddings of $3$-manifolds up to regular homotopy
Spin structures and codimension two embeddings of $3$-manifolds up to regular homotopy
We clarify the structure of the set of regular homotopy classes containing embeddings of a 3-manifold into $5$-space inside the set of all regular homotopy classes of immersions with trivial normal bundles. As a consequence, we show that for a large class of $3$-manifolds $M^3$, the following phenomenon occurs: there …