On planar portraits of manifolds associated with graphs of block decompositions of manifolds (Local and global study of singularity theory of differentiable maps)

Abstract

For a smooth closed manifold M and its stable map f into the plane, the pair mathcal{P}{f} of the image f(M) and the discriminant set of f is called the planar portrait of M through f. In this article, we note an association of mathcal{P}_{f} with a graph representing adjacency of building blocks of M, through examples.