Topology of boundary special generic maps into Euclidean spaces

Abstract: In this paper, we study global properties of boundary special generic maps. A boundary special generic map is defined as a submersion of a compact connected manifold with non-empty boundary into Euclidean spaces, in which all singular points of its restriction to the boundary are boundary definite fold points. In certain dimensions, we characterize the manifolds with boundary that admit such maps up to diffeomorphism.