Complements of discriminants of real parabolic function singularities

TL;DR

This paper provides a comprehensive list of the components of the complements of discriminant varieties for real parabolic singularities and introduces a combinatorial method to classify topological types of non-discriminant morsifications.

Contribution

It offers a conjecturally complete classification of these components and proposes a novel combinatorial approach to enumerate topological types of non-discriminant morsifications.

Findings

List of components of discriminant complements provided

A combinatorial program for topological classification introduced

Strong invariant for components of discriminant complements developed

Abstract

A (conjecturally complete) list of components of complements of discriminant varieties of parabolic singularities of smooth real functions is given. We also promote a combinatorial program that enumerates possible topological types of non-discriminant morsifications of isolated real function singularities and provides a strong invariant of components of complements of discriminant varieties.