Geodesic
On the Nonrepresentability of Functions of Several Variables by Quadratures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 4, pp. 74-85

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The paper completes the construction of a multidimensional topological version of differential Galois theory. We construct a rich class of germs of functions of several variables which is closed under superpositions and other natural operations. The main theorem describes the behavior of the monodromy groups of such germs under the natural operations. As a result, we obtain topological obstructions to the representability of functions by quadratures, which give the strongest known statements about unsolvability of equations in closed form.
Keywords: multivalued function, differential Galois theory, representability by quadratures.
Mots-clés : monodromy group 
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     title = {On the {Nonrepresentability} of {Functions} of {Several} {Variables} by {Quadratures}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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A. G. Khovanskii. On the Nonrepresentability of Functions of Several Variables by Quadratures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 4, pp. 74-85. http://geodesic.mathdoc.fr/item/FAA_2003_37_4_a10/