Complements of discriminants of real boundary singularities

TL;DR

This paper investigates the topology of complements of discriminants in simple real boundary singularities, extending previous work on ordinary function singularities by analyzing connected components and topological features.

Contribution

It generalizes existing results on ordinary singularities to boundary singularities, providing new insights into their topological structure.

Findings

Counted connected components of discriminant complements.

Assigned topological characteristics to these components.

Extended Vassiliev's results to boundary singularities.

Abstract

We study the topology of the complements of discriminants of simple real boundary singularities by counting the connected components of these sets and assigning to them certain topological characteristics. Results of this paper serve as a generalization of those recently acquired by Vassiliev arXiv:2109.12287 for ordinary function singularities.