Projections of hypersurfaces in $mathbb{R}^{4}$ to planes (Theory of singularities of smooth mappings and around it)

Abstract

The aim of this report is to give the singularities of orthogonal projections of a generic embedded hypersurface M in mathbb{R}^{4} with or without boundary, to a 2-dimensional plane. The singularities occurring at interior points have been classified in [11] (see also [14]), and the singularities occurring at the boundary points have been classified in [10]. For the first case, we need to classify map germs from mathbb{R}^{3} to the plane (mathcal{A}-group), and for the second case we need to classify map germs from mathbb{R}^{3} to the plane with the source containing a distinguished plane which is preserved by coordinate changes (B-subgroup). The singularities of such maps measure, for instance, the contact of M with 2-dimensional planes.