The cobordism class of the multiple points of immersions

Abstract

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.Comment: 17 pages; LaTeX2e document, use of eLaTeX recommended, non-standard packages: xy, pxfonts, pbox. Accepted by Algebraic Geometry and Topology. Corrections and clarifications mainly due to the referee of the journa