Functor Calculus and the discriminant method

Reis R, Weiss M

Abstract

The discriminant method is a tool for describing the cohomology, or the homotopy type, of certain spaces of smooth maps with uncomplicated singularities from a smooth compact manifold L to ℝ k. We recast some of it in the language of functor calculus. This reformulation allows us to use the discriminant method in a setting where we wish to impose conditions on the multilocal behavior of smooth maps f : L → ℝk.