Euler characteristic formulas for simplicial maps

In this paper, various Euler characteristic formulas for simplicial maps are obtained, which generalize the Izumiya–Marar formula [ 14 ], the Banchoff triple point formula [ 3 ] and the formula due to Szucs for maps of surfaces into 3-space [ 27 ]. Moreover, we obtain new results about the Euler characteristics of the multiple point sets and the images of generic smooth maps and the numbers of their singularities.

On the number of singularities of a generic surface with boundary in a 3-manifold