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arXiv · 2304.09824

Complements of caustics of real function singularities

V. A. Vassiliev
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Abstract

We study the topology of complements of caustics of function singularities of low codimensions, in particular 1) complete the enumeration of connected components of the complements of caustics of {\em simple} (in the sense of V.Arnold) singularities, in particular find the numbers of these components for the last two classes, $E_7$ and $E_8$, remaining unknown after the works of R.Thom, V.Arnold and V.Sedykh; 2) realize all these components for simple singularities by explicitly constructed functions, and realize their one-dimensional homology and cohomology groups by cycles and cocycles; 3) prove that (in contrast to the case of simple singularities) for some parabolic singularities the two-dimensional homology groups of the complements of their caustics are nontrivial.

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V. A. Vassiliev. 2023-04-19. Complements of caustics of real function singularities. https://arxiv.org/abs/2304.09824

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