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Multidimensional results on the nonrepresentability of functions by quadratures. (English. Russian original) Zbl 1078.32006

Funct. Anal. Appl. 37, No. 4, 302-310 (2003); translation from Funks. Anal. Prilozh. 37, No. 4, 74-85 (2003).
Summary: 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.

MSC:

32B99 Local analytic geometry
41A55 Approximate quadratures
65D30 Numerical integration
58K10 Monodromy on manifolds
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