Views of Real Projective 3-Space by Stable Maps into the Plane

Abstract

ABSTRACTSmooth stable maps into the plane enable us to get the graphical views of the source manifolds. In this article, we present two such maps of the real projective 3-space constructed from typical two projections of a tetrahedron to the plane. Tri- and quarto-sections of the real projective 3-space and Heegaard splittings of genus four and five can be obtained naturally using these maps. A question is posed on views of projective n-spaces of n ⩾ 4.