On projected embeddings and desuspending the \(\alpha\)-invariant (Q1862041)

A map \(f:K\to L\) is called a projected embedding from \(L\times B^s\) if there is an embedding \(F:K\to L\times B^s\) such that \(f=\pi\circ F\), where \(\pi:L\circ B^s\to L\) is the projection. A map \(f:S^p\coprod S^2\to S^m\) is a link map if \(fS^p\cap fS^q=\emptyset\). We apply projected embeddings to desuspending the \(\alpha\)-invariant of link maps and to embeddings of double covers into Euclidean space.