Fold maps on low dimensional manifolds

2021. 09. 28. 10:30
Kalmár Boldizsár

We give sufficient and necessary conditions for the existence of a fold map from a closed $n$-dimensional manifold to $\mathbb R^{n-1}$ with prescribed singular set for $5\leq n\leq 8$. We obtain relations between topological properties of the source manifold like the Euler characteristic and the signature and some global topological properties of the fold singular set like the self-intersection number. We use obstruction theory and the homotopy principle for fold maps.