Obstructions for Morin and fold maps: Stiefel-Whitney classes and Euler characteristics of singularity loci

László M. Fehér, Ákos K. Matszangosz

For a singularity type $\hat{I}\cdot$, let the $\hat{I}\cdot$-avoiding number of an $n$-dimensional manifold $M$ be the lowest $k$ for which there is a map $M\to {\mathbb{R}}^{n+k}$ without $\hat{I}\cdot$ type sin…