Morse theory, Bruhat cells and Unitriangular geometry

Strong Morse function is a Morse function with pairwise different critical values. For such a function we construct a collection of numbers, which is a (smooth) topological invariant of the strong Morse function.
Algebraically our construction is a close relative of the construction of Bruhat cells and belongs to Unitriangular geometry. We will present a generalization of determinant of any linear map between finite dimensional vector spaces.
Talk based on a joint work with Misha Temkin.