Topological properties of caustics in five-dimensional spaces

Vyacheslav D. Sedykh

doi:10.4213/sm10131e

paper

Topological properties of caustics in five-dimensional spaces

arXiv:2401.09215 · doi:10.4213/sm10131e

Abstract

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 $D_{5} A_{2}, A_{4} A_{3}, A_{4} A_{2}^{2}$ of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers $D_{4}^{+} A_{3} + D_{4}^{-} A_{3} + E_{6}$ , $D_{4}^{+} A_{2}^{2} + D_{4}^{-} A_{2}^{2} + \frac{1}{2} A_{4} A_{3}$ are even as well.

11 pages. arXiv admin note: text overlap with arXiv:2310.15748