Speaker: Liam Kahmeyer

Abstract: In a pair of talks, I will give a solution to an open problem posed by Osamu Saeki. In my first talk, I will discuss so-called ‘abstract singular set diagrams’, along with proving some important properties, for generic smooth maps from an m-manifold to a 2-manifold. I will also define chessboard functions, provide examples, and use them to construct orientations and co-orientations of the singular set of smooth generic maps from an m-manifold to an n-manifolds, with (m – n) non-negative. Viewing the singular set of generic smooth maps to 2-manifolds as a singular set diagram, equipped with an orientation induced from a chessboard function, is crucial in solving the Saeki problem.