On local structures of the singularities $A_ k\;D_ k$ and $E_ k$ of smooth maps

Abstract:

In studying the singularities of type ${A_k}$ of smooth maps between manifolds $N$ and $P$ the Boardman manifold ${\sum ^{i,1, \ldots ,10}}$ in ${J^\infty } (N,P)$ has been very useful. We will construct the submanifolds $\sum {D_k}$ and $\Sigma {E_k}$ in ${J^\infty } (N,P)$ playing the similar role for singularities ${D_k}$ and ${E_k}$ and study their properties in its process.