Topological properties of caustics in five-dimensional spaces

Abstract

We present a list of universal linear relations between the Euler characteristics of manifolds consisting of multisingularities of a generic Lagrangian map into a five-dimensional space. From these relations it follows, in particular, that the numbers $D_5A_2$, $A_4A_3$, $A_4A^2_2$ of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers $D^+_4 A_3 + D^-_4 A3 + E_6 $ and $D^+_4 A^2_2 + D^-_4 A^2_2 + \frac12 A_4A_3$ are also even.