arXiv subjects
Publications and source records attributed to Vyacheslav D. Sedykh.
We prove that the complement to the caustic of a stable Lagrangian map germ of type $E_6^\pm$ has seven connected components, six of which are contractible and one is homotopy equivalent to a circle. The inverse image of the noncontractible component under this map has three connected components. The restriction of the map to one of them is a two-sheeted covering; the restriction to each of the other two is a diffeomorphism.
The formula for the calculation of the adjacency indices of types $D_μ^\pm$ Legendrian monosingularities to multisingularities of types $A_{μ_1}^{k_1}\dots A_{μ_p}^{k_p}$ is obtained in the paper. Namely the number of strata of a given type $A_{μ_1}^{k_1}\dots A_{μ_p}^{k_p}$ in the discriminant of a real simple singularity of any of types $D_μ^\pm$ is calculated.
We give 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 $D_4^+A_3+D_4^-A_3+E_6$, $D_4^+A_2^2+D_4^-A_2^2+\frac12A_4A_3$ are even as well.