Geodesic
On topological invariants of real algebraic functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 3, pp. 4-15

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A natural covering responsible for the complexity of the ramification of roots of the general real polynomial equation is considered, and the homology groups of its base are calculated; for equations of degree $\le 5$, a complete description of the topology of this base is given.
Mots-clés : ramification, discriminant
Keywords: real algebraic function, Schwarz genus. 
@article{FAA_2011_45_3_a1,
     author = {V. A. Vassiliev},
     title = {On topological invariants of real algebraic functions},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {4--15},
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2011_45_3_a1/}
}
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V. A. Vassiliev. On topological invariants of real algebraic functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 45 (2011) no. 3, pp. 4-15. http://geodesic.mathdoc.fr/item/FAA_2011_45_3_a1/