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arXiv · 2311.11113

Isotopy classification of Morse polynomials of degree 4 in ${\mathbb R}^2$

V. A. Vassiliev
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Abstract

We introduce a system of invariants of isotopy classes of Morse polynomials ${\mathbb R}^2 \to {\mathbb R}^1$, prove its completeness for polynomials of degrees $\leq 4$, calculate all 71 possible values of these invariants for the case of degree 4, and realize them by concrete Morse polynomials. Also we count all 45460 classes of {\em strictly} Morse polynomials of degree four with the maximal possible number (nine) of real critical points. Keywords: real algebraic geometry, Morse function, Milnor fiber, Coxeter-Dynkin graph, vanishing cycle, topological invariant, surgery, Lyashko--Looijenga map.

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V. A. Vassiliev. 2023-11-18. Isotopy classification of Morse polynomials of degree 4 in ${\mathbb R}^2$. https://arxiv.org/abs/2311.11113

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