Abstract:
We present a list of universal linear relations between the Euler characteristics of manifolds of multisingularities of a generic Lagrangian map to a five-dimensional space. From these relations it follows, in particular, that the numbers $D_5A_2$, $A_4A_3$ and $A_4A_2^2$ of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers $D_4^+A_3+D_4^-A_3+E_6$ and $D_4^+A_2^2+D_4^-A_2^2+\frac12A_4A_3$ are also even.
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