Provides the complete list of connected components of Morse functions in deformations of J10 singularities, finishing the isotopy classification of parabolic real function singularities.
Vassiliev, Complements of caustics of real function singularities , Journal of Singularities, 27 (2024), 47–67 , arXiv: 2304.09824
2 Pith papers cite this work. Polarity classification is still indexing.
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A complete system of isotopy invariants is proven for Morse polynomials of degree ≤4 over the reals, with explicit realization of all 71 classes for degree 4 and a count of maximal-critical-point classes up to reflection.
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Complements of caustics of the real $J_{10}$ singularities
Provides the complete list of connected components of Morse functions in deformations of J10 singularities, finishing the isotopy classification of parabolic real function singularities.
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Isotopy classification of Morse polynomials of degree 4 in ${\mathbb R}^2$
A complete system of isotopy invariants is proven for Morse polynomials of degree ≤4 over the reals, with explicit realization of all 71 classes for degree 4 and a count of maximal-critical-point classes up to reflection.