Geodesic
Topological classification of Morse polynomials
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 40-55

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The topological classification is discussed for real polynomials of degree 4 in two real independent variables whose critical points and critical values are all different. It is proved that among the 17746 topological types of smooth functions with the same number of critical points, at most 426 types are realizable by polynomials of degree 4. 
@article{TM_2010_268_a3,
     author = {V. I. Arnold},
     title = {Topological classification of {Morse} polynomials},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {40--55},
     publisher = {mathdoc},
     volume = {268},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_268_a3/}
}
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V. I. Arnold. Topological classification of Morse polynomials. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 40-55. http://geodesic.mathdoc.fr/item/TM_2010_268_a3/