The cobordism class of the multiple points of immersions
  Let f: M -> N be an even codimensional immersion between smooth manifolds. We derive an explicit formula for the Pontrjagin numbers and signature of the multiple point manifolds in terms of singular cohomology of M and N, the maps induced between these by f and the characteristic classes of the normal bundle.   The main trick is to solve a recursion in cohomology by the use of (generalized) formal power series. 
G\'abor Braun